KILLED
proof of input_mvTxAqe4JS.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


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

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(4) CpxTRS
(5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxWeightedTrs
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTypedWeightedTrs
    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
        (11) NarrowingProof [BOTH BOUNDS(ID, ID), 1619 ms]
        (12) CpxTypedWeightedCompleteTrs
        (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (14) CpxRNTS
        (15) InliningProof [UPPER BOUND(ID), 742 ms]
        (16) CpxRNTS
        (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (18) CpxRNTS
    (19) CompletionProof [UPPER BOUND(ID), 0 ms]
    (20) CpxTypedWeightedCompleteTrs
        (21) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 12 ms]
        (22) CpxRNTS
(23) CpxTrsToCdtProof [UPPER BOUND(ID), 57 ms]
(24) CdtProblem
    (25) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (26) CdtProblem
    (27) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (28) CdtProblem
    (29) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms]
    (30) CdtProblem
    (31) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (32) CdtProblem
    (33) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms]
    (34) CdtProblem
    (35) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (36) CdtProblem
    (37) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms]
    (38) CdtProblem
    (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms]
    (42) CdtProblem
    (43) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (44) CdtProblem
    (45) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CdtProblem
    (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms]
    (60) CdtProblem
    (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 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), 39 ms]
    (72) CdtProblem
    (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms]
    (76) CdtProblem
    (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms]
    (80) CdtProblem
    (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms]
    (82) CdtProblem
    (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 51 ms]
    (84) CdtProblem
    (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 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), 0 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), 44 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), 52 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), 61 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), 71 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), 65 ms]
    (124) CdtProblem
    (125) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 2 ms]
    (126) CdtProblem
    (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (128) CdtProblem
    (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 59 ms]
    (130) CdtProblem
    (131) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 8 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), 63 ms]
    (142) CdtProblem
    (143) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 10 ms]
    (144) CdtProblem
    (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (146) CdtProblem
    (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 115 ms]
    (148) CdtProblem
    (149) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (150) CdtProblem
    (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (152) CdtProblem
    (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 154 ms]
    (154) CdtProblem
    (155) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (156) CdtProblem
    (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (158) CdtProblem
    (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 348 ms]
    (160) CdtProblem
    (161) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (162) CdtProblem
    (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (164) CdtProblem
    (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 440 ms]
    (166) CdtProblem
    (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 46 ms]
    (168) CdtProblem
    (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 203 ms]
    (170) CdtProblem
    (171) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 26 ms]
    (172) CdtProblem
    (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (174) CdtProblem
    (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms]
    (176) CdtProblem
    (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 21 ms]
    (178) CdtProblem
    (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 115 ms]
    (180) CdtProblem
    (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (182) CdtProblem
    (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 63 ms]
    (184) CdtProblem
    (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 15 ms]
    (186) CdtProblem
    (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 62 ms]
    (188) CdtProblem
    (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (190) CdtProblem
    (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms]
    (192) CdtProblem
    (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 19 ms]
    (194) CdtProblem
    (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 101 ms]
    (196) CdtProblem
    (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms]
    (198) CdtProblem
    (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 62 ms]
    (200) CdtProblem
    (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (202) CdtProblem
    (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 125 ms]
    (204) CdtProblem
    (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 5 ms]
    (206) CdtProblem
    (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 103 ms]
    (208) CdtProblem
    (209) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (210) CdtProblem
    (211) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 78 ms]
    (212) CdtProblem
    (213) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (214) CdtProblem
    (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 145 ms]
    (216) CdtProblem
    (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (218) CdtProblem


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

(0)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   a__zeros -> cons(0, zeros)
   a__U11(tt, V1) -> a__U12(a__isNatList(V1))
   a__U12(tt) -> tt
   a__U21(tt, V1) -> a__U22(a__isNat(V1))
   a__U22(tt) -> tt
   a__U31(tt, V) -> a__U32(a__isNatList(V))
   a__U32(tt) -> tt
   a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2)
   a__U42(tt, V2) -> a__U43(a__isNatIList(V2))
   a__U43(tt) -> tt
   a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2)
   a__U52(tt, V2) -> a__U53(a__isNatList(V2))
   a__U53(tt) -> tt
   a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2)
   a__U62(tt, V2) -> a__U63(a__isNatIList(V2))
   a__U63(tt) -> tt
   a__U71(tt, L) -> s(a__length(mark(L)))
   a__U81(tt) -> nil
   a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL))
   a__and(tt, X) -> mark(X)
   a__isNat(0) -> tt
   a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1)
   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
   a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2))
   a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2))
   a__isNatKind(0) -> tt
   a__isNatKind(length(V1)) -> a__isNatIListKind(V1)
   a__isNatKind(s(V1)) -> a__isNatKind(V1)
   a__isNatList(nil) -> tt
   a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
   a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
   a__length(nil) -> 0
   a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L)
   a__take(0, IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL)))
   a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N)
   mark(zeros) -> a__zeros
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
   mark(U12(X)) -> a__U12(mark(X))
   mark(isNatList(X)) -> a__isNatList(X)
   mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
   mark(U22(X)) -> a__U22(mark(X))
   mark(isNat(X)) -> a__isNat(X)
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
   mark(U32(X)) -> a__U32(mark(X))
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
   mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
   mark(U43(X)) -> a__U43(mark(X))
   mark(isNatIList(X)) -> a__isNatIList(X)
   mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
   mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
   mark(U53(X)) -> a__U53(mark(X))
   mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3)
   mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
   mark(U63(X)) -> a__U63(mark(X))
   mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
   mark(length(X)) -> a__length(mark(X))
   mark(U81(X)) -> a__U81(mark(X))
   mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
   mark(and(X1, X2)) -> a__and(mark(X1), X2)
   mark(isNatIListKind(X)) -> a__isNatIListKind(X)
   mark(isNatKind(X)) -> a__isNatKind(X)
   mark(cons(X1, X2)) -> cons(mark(X1), X2)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(X)) -> s(mark(X))
   mark(nil) -> nil
   a__zeros -> zeros
   a__U11(X1, X2) -> U11(X1, X2)
   a__U12(X) -> U12(X)
   a__isNatList(X) -> isNatList(X)
   a__U21(X1, X2) -> U21(X1, X2)
   a__U22(X) -> U22(X)
   a__isNat(X) -> isNat(X)
   a__U31(X1, X2) -> U31(X1, X2)
   a__U32(X) -> U32(X)
   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
   a__U42(X1, X2) -> U42(X1, X2)
   a__U43(X) -> U43(X)
   a__isNatIList(X) -> isNatIList(X)
   a__U51(X1, X2, X3) -> U51(X1, X2, X3)
   a__U52(X1, X2) -> U52(X1, X2)
   a__U53(X) -> U53(X)
   a__U61(X1, X2, X3) -> U61(X1, X2, X3)
   a__U62(X1, X2) -> U62(X1, X2)
   a__U63(X) -> U63(X)
   a__U71(X1, X2) -> U71(X1, X2)
   a__length(X) -> length(X)
   a__U81(X) -> U81(X)
   a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
   a__take(X1, X2) -> take(X1, X2)
   a__and(X1, X2) -> and(X1, X2)
   a__isNatIListKind(X) -> isNatIListKind(X)
   a__isNatKind(X) -> isNatKind(X)

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

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

(2)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   a__zeros -> cons(0', zeros)
   a__U11(tt, V1) -> a__U12(a__isNatList(V1))
   a__U12(tt) -> tt
   a__U21(tt, V1) -> a__U22(a__isNat(V1))
   a__U22(tt) -> tt
   a__U31(tt, V) -> a__U32(a__isNatList(V))
   a__U32(tt) -> tt
   a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2)
   a__U42(tt, V2) -> a__U43(a__isNatIList(V2))
   a__U43(tt) -> tt
   a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2)
   a__U52(tt, V2) -> a__U53(a__isNatList(V2))
   a__U53(tt) -> tt
   a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2)
   a__U62(tt, V2) -> a__U63(a__isNatIList(V2))
   a__U63(tt) -> tt
   a__U71(tt, L) -> s(a__length(mark(L)))
   a__U81(tt) -> nil
   a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL))
   a__and(tt, X) -> mark(X)
   a__isNat(0') -> tt
   a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1)
   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
   a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2))
   a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2))
   a__isNatKind(0') -> tt
   a__isNatKind(length(V1)) -> a__isNatIListKind(V1)
   a__isNatKind(s(V1)) -> a__isNatKind(V1)
   a__isNatList(nil) -> tt
   a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
   a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
   a__length(nil) -> 0'
   a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L)
   a__take(0', IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL)))
   a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N)
   mark(zeros) -> a__zeros
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
   mark(U12(X)) -> a__U12(mark(X))
   mark(isNatList(X)) -> a__isNatList(X)
   mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
   mark(U22(X)) -> a__U22(mark(X))
   mark(isNat(X)) -> a__isNat(X)
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
   mark(U32(X)) -> a__U32(mark(X))
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
   mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
   mark(U43(X)) -> a__U43(mark(X))
   mark(isNatIList(X)) -> a__isNatIList(X)
   mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
   mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
   mark(U53(X)) -> a__U53(mark(X))
   mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3)
   mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
   mark(U63(X)) -> a__U63(mark(X))
   mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
   mark(length(X)) -> a__length(mark(X))
   mark(U81(X)) -> a__U81(mark(X))
   mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
   mark(and(X1, X2)) -> a__and(mark(X1), X2)
   mark(isNatIListKind(X)) -> a__isNatIListKind(X)
   mark(isNatKind(X)) -> a__isNatKind(X)
   mark(cons(X1, X2)) -> cons(mark(X1), X2)
   mark(0') -> 0'
   mark(tt) -> tt
   mark(s(X)) -> s(mark(X))
   mark(nil) -> nil
   a__zeros -> zeros
   a__U11(X1, X2) -> U11(X1, X2)
   a__U12(X) -> U12(X)
   a__isNatList(X) -> isNatList(X)
   a__U21(X1, X2) -> U21(X1, X2)
   a__U22(X) -> U22(X)
   a__isNat(X) -> isNat(X)
   a__U31(X1, X2) -> U31(X1, X2)
   a__U32(X) -> U32(X)
   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
   a__U42(X1, X2) -> U42(X1, X2)
   a__U43(X) -> U43(X)
   a__isNatIList(X) -> isNatIList(X)
   a__U51(X1, X2, X3) -> U51(X1, X2, X3)
   a__U52(X1, X2) -> U52(X1, X2)
   a__U53(X) -> U53(X)
   a__U61(X1, X2, X3) -> U61(X1, X2, X3)
   a__U62(X1, X2) -> U62(X1, X2)
   a__U63(X) -> U63(X)
   a__U71(X1, X2) -> U71(X1, X2)
   a__length(X) -> length(X)
   a__U81(X) -> U81(X)
   a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
   a__take(X1, X2) -> take(X1, X2)
   a__and(X1, X2) -> and(X1, X2)
   a__isNatIListKind(X) -> isNatIListKind(X)
   a__isNatKind(X) -> isNatKind(X)

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

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

(4)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   a__zeros -> cons(0, zeros)
   a__U11(tt, V1) -> a__U12(a__isNatList(V1))
   a__U12(tt) -> tt
   a__U21(tt, V1) -> a__U22(a__isNat(V1))
   a__U22(tt) -> tt
   a__U31(tt, V) -> a__U32(a__isNatList(V))
   a__U32(tt) -> tt
   a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2)
   a__U42(tt, V2) -> a__U43(a__isNatIList(V2))
   a__U43(tt) -> tt
   a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2)
   a__U52(tt, V2) -> a__U53(a__isNatList(V2))
   a__U53(tt) -> tt
   a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2)
   a__U62(tt, V2) -> a__U63(a__isNatIList(V2))
   a__U63(tt) -> tt
   a__U71(tt, L) -> s(a__length(mark(L)))
   a__U81(tt) -> nil
   a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL))
   a__and(tt, X) -> mark(X)
   a__isNat(0) -> tt
   a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1)
   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1)
   a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2))
   a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2))
   a__isNatKind(0) -> tt
   a__isNatKind(length(V1)) -> a__isNatIListKind(V1)
   a__isNatKind(s(V1)) -> a__isNatKind(V1)
   a__isNatList(nil) -> tt
   a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
   a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2)
   a__length(nil) -> 0
   a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L)
   a__take(0, IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL)))
   a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N)
   mark(zeros) -> a__zeros
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
   mark(U12(X)) -> a__U12(mark(X))
   mark(isNatList(X)) -> a__isNatList(X)
   mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
   mark(U22(X)) -> a__U22(mark(X))
   mark(isNat(X)) -> a__isNat(X)
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
   mark(U32(X)) -> a__U32(mark(X))
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
   mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
   mark(U43(X)) -> a__U43(mark(X))
   mark(isNatIList(X)) -> a__isNatIList(X)
   mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
   mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
   mark(U53(X)) -> a__U53(mark(X))
   mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3)
   mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
   mark(U63(X)) -> a__U63(mark(X))
   mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
   mark(length(X)) -> a__length(mark(X))
   mark(U81(X)) -> a__U81(mark(X))
   mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4)
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
   mark(and(X1, X2)) -> a__and(mark(X1), X2)
   mark(isNatIListKind(X)) -> a__isNatIListKind(X)
   mark(isNatKind(X)) -> a__isNatKind(X)
   mark(cons(X1, X2)) -> cons(mark(X1), X2)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(X)) -> s(mark(X))
   mark(nil) -> nil
   a__zeros -> zeros
   a__U11(X1, X2) -> U11(X1, X2)
   a__U12(X) -> U12(X)
   a__isNatList(X) -> isNatList(X)
   a__U21(X1, X2) -> U21(X1, X2)
   a__U22(X) -> U22(X)
   a__isNat(X) -> isNat(X)
   a__U31(X1, X2) -> U31(X1, X2)
   a__U32(X) -> U32(X)
   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
   a__U42(X1, X2) -> U42(X1, X2)
   a__U43(X) -> U43(X)
   a__isNatIList(X) -> isNatIList(X)
   a__U51(X1, X2, X3) -> U51(X1, X2, X3)
   a__U52(X1, X2) -> U52(X1, X2)
   a__U53(X) -> U53(X)
   a__U61(X1, X2, X3) -> U61(X1, X2, X3)
   a__U62(X1, X2) -> U62(X1, X2)
   a__U63(X) -> U63(X)
   a__U71(X1, X2) -> U71(X1, X2)
   a__length(X) -> length(X)
   a__U81(X) -> U81(X)
   a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4)
   a__take(X1, X2) -> take(X1, X2)
   a__and(X1, X2) -> and(X1, X2)
   a__isNatIListKind(X) -> isNatIListKind(X)
   a__isNatKind(X) -> isNatKind(X)

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

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

(6)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   a__zeros -> cons(0, zeros) [1]
   a__U11(tt, V1) -> a__U12(a__isNatList(V1)) [1]
   a__U12(tt) -> tt [1]
   a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1]
   a__U22(tt) -> tt [1]
   a__U31(tt, V) -> a__U32(a__isNatList(V)) [1]
   a__U32(tt) -> tt [1]
   a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2) [1]
   a__U42(tt, V2) -> a__U43(a__isNatIList(V2)) [1]
   a__U43(tt) -> tt [1]
   a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2) [1]
   a__U52(tt, V2) -> a__U53(a__isNatList(V2)) [1]
   a__U53(tt) -> tt [1]
   a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2) [1]
   a__U62(tt, V2) -> a__U63(a__isNatIList(V2)) [1]
   a__U63(tt) -> tt [1]
   a__U71(tt, L) -> s(a__length(mark(L))) [1]
   a__U81(tt) -> nil [1]
   a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1]
   a__and(tt, X) -> mark(X) [1]
   a__isNat(0) -> tt [1]
   a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) [1]
   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1]
   a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) [1]
   a__isNatIList(zeros) -> tt [1]
   a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1]
   a__isNatIListKind(nil) -> tt [1]
   a__isNatIListKind(zeros) -> tt [1]
   a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1]
   a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1]
   a__isNatKind(0) -> tt [1]
   a__isNatKind(length(V1)) -> a__isNatIListKind(V1) [1]
   a__isNatKind(s(V1)) -> a__isNatKind(V1) [1]
   a__isNatList(nil) -> tt [1]
   a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1]
   a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1]
   a__length(nil) -> 0 [1]
   a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) [1]
   a__take(0, IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) [1]
   a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) [1]
   mark(zeros) -> a__zeros [1]
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1]
   mark(U12(X)) -> a__U12(mark(X)) [1]
   mark(isNatList(X)) -> a__isNatList(X) [1]
   mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1]
   mark(U22(X)) -> a__U22(mark(X)) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1]
   mark(U32(X)) -> a__U32(mark(X)) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(U42(X1, X2)) -> a__U42(mark(X1), X2) [1]
   mark(U43(X)) -> a__U43(mark(X)) [1]
   mark(isNatIList(X)) -> a__isNatIList(X) [1]
   mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) [1]
   mark(U52(X1, X2)) -> a__U52(mark(X1), X2) [1]
   mark(U53(X)) -> a__U53(mark(X)) [1]
   mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) [1]
   mark(U62(X1, X2)) -> a__U62(mark(X1), X2) [1]
   mark(U63(X)) -> a__U63(mark(X)) [1]
   mark(U71(X1, X2)) -> a__U71(mark(X1), X2) [1]
   mark(length(X)) -> a__length(mark(X)) [1]
   mark(U81(X)) -> a__U81(mark(X)) [1]
   mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) [1]
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), X2) [1]
   mark(isNatIListKind(X)) -> a__isNatIListKind(X) [1]
   mark(isNatKind(X)) -> a__isNatKind(X) [1]
   mark(cons(X1, X2)) -> cons(mark(X1), X2) [1]
   mark(0) -> 0 [1]
   mark(tt) -> tt [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(nil) -> nil [1]
   a__zeros -> zeros [1]
   a__U11(X1, X2) -> U11(X1, X2) [1]
   a__U12(X) -> U12(X) [1]
   a__isNatList(X) -> isNatList(X) [1]
   a__U21(X1, X2) -> U21(X1, X2) [1]
   a__U22(X) -> U22(X) [1]
   a__isNat(X) -> isNat(X) [1]
   a__U31(X1, X2) -> U31(X1, X2) [1]
   a__U32(X) -> U32(X) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__U42(X1, X2) -> U42(X1, X2) [1]
   a__U43(X) -> U43(X) [1]
   a__isNatIList(X) -> isNatIList(X) [1]
   a__U51(X1, X2, X3) -> U51(X1, X2, X3) [1]
   a__U52(X1, X2) -> U52(X1, X2) [1]
   a__U53(X) -> U53(X) [1]
   a__U61(X1, X2, X3) -> U61(X1, X2, X3) [1]
   a__U62(X1, X2) -> U62(X1, X2) [1]
   a__U63(X) -> U63(X) [1]
   a__U71(X1, X2) -> U71(X1, X2) [1]
   a__length(X) -> length(X) [1]
   a__U81(X) -> U81(X) [1]
   a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) [1]
   a__take(X1, X2) -> take(X1, X2) [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNatIListKind(X) -> isNatIListKind(X) [1]
   a__isNatKind(X) -> isNatKind(X) [1]

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

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

(8)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   a__zeros -> cons(0, zeros) [1]
   a__U11(tt, V1) -> a__U12(a__isNatList(V1)) [1]
   a__U12(tt) -> tt [1]
   a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1]
   a__U22(tt) -> tt [1]
   a__U31(tt, V) -> a__U32(a__isNatList(V)) [1]
   a__U32(tt) -> tt [1]
   a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2) [1]
   a__U42(tt, V2) -> a__U43(a__isNatIList(V2)) [1]
   a__U43(tt) -> tt [1]
   a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2) [1]
   a__U52(tt, V2) -> a__U53(a__isNatList(V2)) [1]
   a__U53(tt) -> tt [1]
   a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2) [1]
   a__U62(tt, V2) -> a__U63(a__isNatIList(V2)) [1]
   a__U63(tt) -> tt [1]
   a__U71(tt, L) -> s(a__length(mark(L))) [1]
   a__U81(tt) -> nil [1]
   a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1]
   a__and(tt, X) -> mark(X) [1]
   a__isNat(0) -> tt [1]
   a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) [1]
   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1]
   a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) [1]
   a__isNatIList(zeros) -> tt [1]
   a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1]
   a__isNatIListKind(nil) -> tt [1]
   a__isNatIListKind(zeros) -> tt [1]
   a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1]
   a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1]
   a__isNatKind(0) -> tt [1]
   a__isNatKind(length(V1)) -> a__isNatIListKind(V1) [1]
   a__isNatKind(s(V1)) -> a__isNatKind(V1) [1]
   a__isNatList(nil) -> tt [1]
   a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1]
   a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1]
   a__length(nil) -> 0 [1]
   a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) [1]
   a__take(0, IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) [1]
   a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) [1]
   mark(zeros) -> a__zeros [1]
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1]
   mark(U12(X)) -> a__U12(mark(X)) [1]
   mark(isNatList(X)) -> a__isNatList(X) [1]
   mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1]
   mark(U22(X)) -> a__U22(mark(X)) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1]
   mark(U32(X)) -> a__U32(mark(X)) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(U42(X1, X2)) -> a__U42(mark(X1), X2) [1]
   mark(U43(X)) -> a__U43(mark(X)) [1]
   mark(isNatIList(X)) -> a__isNatIList(X) [1]
   mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) [1]
   mark(U52(X1, X2)) -> a__U52(mark(X1), X2) [1]
   mark(U53(X)) -> a__U53(mark(X)) [1]
   mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) [1]
   mark(U62(X1, X2)) -> a__U62(mark(X1), X2) [1]
   mark(U63(X)) -> a__U63(mark(X)) [1]
   mark(U71(X1, X2)) -> a__U71(mark(X1), X2) [1]
   mark(length(X)) -> a__length(mark(X)) [1]
   mark(U81(X)) -> a__U81(mark(X)) [1]
   mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) [1]
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), X2) [1]
   mark(isNatIListKind(X)) -> a__isNatIListKind(X) [1]
   mark(isNatKind(X)) -> a__isNatKind(X) [1]
   mark(cons(X1, X2)) -> cons(mark(X1), X2) [1]
   mark(0) -> 0 [1]
   mark(tt) -> tt [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(nil) -> nil [1]
   a__zeros -> zeros [1]
   a__U11(X1, X2) -> U11(X1, X2) [1]
   a__U12(X) -> U12(X) [1]
   a__isNatList(X) -> isNatList(X) [1]
   a__U21(X1, X2) -> U21(X1, X2) [1]
   a__U22(X) -> U22(X) [1]
   a__isNat(X) -> isNat(X) [1]
   a__U31(X1, X2) -> U31(X1, X2) [1]
   a__U32(X) -> U32(X) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__U42(X1, X2) -> U42(X1, X2) [1]
   a__U43(X) -> U43(X) [1]
   a__isNatIList(X) -> isNatIList(X) [1]
   a__U51(X1, X2, X3) -> U51(X1, X2, X3) [1]
   a__U52(X1, X2) -> U52(X1, X2) [1]
   a__U53(X) -> U53(X) [1]
   a__U61(X1, X2, X3) -> U61(X1, X2, X3) [1]
   a__U62(X1, X2) -> U62(X1, X2) [1]
   a__U63(X) -> U63(X) [1]
   a__U71(X1, X2) -> U71(X1, X2) [1]
   a__length(X) -> length(X) [1]
   a__U81(X) -> U81(X) [1]
   a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) [1]
   a__take(X1, X2) -> take(X1, X2) [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNatIListKind(X) -> isNatIListKind(X) [1]
   a__isNatKind(X) -> isNatKind(X) [1]

The TRS has the following type information:
a__zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
cons :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
0 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
tt :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
s :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
mark :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
nil :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91

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

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

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

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:
none

(c) The following functions are completely defined:

   mark_1
   a__isNat_1
   a__and_2
   a__isNatIList_1
   a__isNatList_1
   a__isNatIListKind_1
   a__isNatKind_1
   a__U22_1
   a__U53_1
   a__U32_1
   a__U63_1
   a__length_1
   a__take_2
   a__zeros
   a__U81_1
   a__U71_2
   a__U31_2
   a__U62_2
   a__U61_3
   a__U42_2
   a__U91_4
   a__U21_2
   a__U43_1
   a__U12_1
   a__U51_3
   a__U41_3
   a__U11_2
   a__U52_2

Due to the following rules being added:
none

And the following fresh constants: none

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

(10)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   a__zeros -> cons(0, zeros) [1]
   a__U11(tt, V1) -> a__U12(a__isNatList(V1)) [1]
   a__U12(tt) -> tt [1]
   a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1]
   a__U22(tt) -> tt [1]
   a__U31(tt, V) -> a__U32(a__isNatList(V)) [1]
   a__U32(tt) -> tt [1]
   a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2) [1]
   a__U42(tt, V2) -> a__U43(a__isNatIList(V2)) [1]
   a__U43(tt) -> tt [1]
   a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2) [1]
   a__U52(tt, V2) -> a__U53(a__isNatList(V2)) [1]
   a__U53(tt) -> tt [1]
   a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2) [1]
   a__U62(tt, V2) -> a__U63(a__isNatIList(V2)) [1]
   a__U63(tt) -> tt [1]
   a__U71(tt, L) -> s(a__length(mark(L))) [1]
   a__U81(tt) -> nil [1]
   a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1]
   a__and(tt, X) -> mark(X) [1]
   a__isNat(0) -> tt [1]
   a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) [1]
   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1]
   a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) [1]
   a__isNatIList(zeros) -> tt [1]
   a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1]
   a__isNatIListKind(nil) -> tt [1]
   a__isNatIListKind(zeros) -> tt [1]
   a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1]
   a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1]
   a__isNatKind(0) -> tt [1]
   a__isNatKind(length(V1)) -> a__isNatIListKind(V1) [1]
   a__isNatKind(s(V1)) -> a__isNatKind(V1) [1]
   a__isNatList(nil) -> tt [1]
   a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1]
   a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1]
   a__length(nil) -> 0 [1]
   a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) [1]
   a__take(0, IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) [1]
   a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) [1]
   mark(zeros) -> a__zeros [1]
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1]
   mark(U12(X)) -> a__U12(mark(X)) [1]
   mark(isNatList(X)) -> a__isNatList(X) [1]
   mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1]
   mark(U22(X)) -> a__U22(mark(X)) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1]
   mark(U32(X)) -> a__U32(mark(X)) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(U42(X1, X2)) -> a__U42(mark(X1), X2) [1]
   mark(U43(X)) -> a__U43(mark(X)) [1]
   mark(isNatIList(X)) -> a__isNatIList(X) [1]
   mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) [1]
   mark(U52(X1, X2)) -> a__U52(mark(X1), X2) [1]
   mark(U53(X)) -> a__U53(mark(X)) [1]
   mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) [1]
   mark(U62(X1, X2)) -> a__U62(mark(X1), X2) [1]
   mark(U63(X)) -> a__U63(mark(X)) [1]
   mark(U71(X1, X2)) -> a__U71(mark(X1), X2) [1]
   mark(length(X)) -> a__length(mark(X)) [1]
   mark(U81(X)) -> a__U81(mark(X)) [1]
   mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) [1]
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), X2) [1]
   mark(isNatIListKind(X)) -> a__isNatIListKind(X) [1]
   mark(isNatKind(X)) -> a__isNatKind(X) [1]
   mark(cons(X1, X2)) -> cons(mark(X1), X2) [1]
   mark(0) -> 0 [1]
   mark(tt) -> tt [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(nil) -> nil [1]
   a__zeros -> zeros [1]
   a__U11(X1, X2) -> U11(X1, X2) [1]
   a__U12(X) -> U12(X) [1]
   a__isNatList(X) -> isNatList(X) [1]
   a__U21(X1, X2) -> U21(X1, X2) [1]
   a__U22(X) -> U22(X) [1]
   a__isNat(X) -> isNat(X) [1]
   a__U31(X1, X2) -> U31(X1, X2) [1]
   a__U32(X) -> U32(X) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__U42(X1, X2) -> U42(X1, X2) [1]
   a__U43(X) -> U43(X) [1]
   a__isNatIList(X) -> isNatIList(X) [1]
   a__U51(X1, X2, X3) -> U51(X1, X2, X3) [1]
   a__U52(X1, X2) -> U52(X1, X2) [1]
   a__U53(X) -> U53(X) [1]
   a__U61(X1, X2, X3) -> U61(X1, X2, X3) [1]
   a__U62(X1, X2) -> U62(X1, X2) [1]
   a__U63(X) -> U63(X) [1]
   a__U71(X1, X2) -> U71(X1, X2) [1]
   a__length(X) -> length(X) [1]
   a__U81(X) -> U81(X) [1]
   a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) [1]
   a__take(X1, X2) -> take(X1, X2) [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNatIListKind(X) -> isNatIListKind(X) [1]
   a__isNatKind(X) -> isNatKind(X) [1]

The TRS has the following type information:
a__zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
cons :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
0 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
tt :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
s :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
mark :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
nil :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91

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

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

(12)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   a__zeros -> cons(0, zeros) [1]
   a__U11(tt, nil) -> a__U12(tt) [2]
   a__U11(tt, cons(V1', V2')) -> a__U12(a__U51(a__and(a__isNatKind(V1'), isNatIListKind(V2')), V1', V2')) [2]
   a__U11(tt, take(V1'', V2'')) -> a__U12(a__U61(a__and(a__isNatKind(V1''), isNatIListKind(V2'')), V1'', V2'')) [2]
   a__U11(tt, V1) -> a__U12(isNatList(V1)) [2]
   a__U12(tt) -> tt [1]
   a__U21(tt, 0) -> a__U22(tt) [2]
   a__U21(tt, length(V11)) -> a__U22(a__U11(a__isNatIListKind(V11), V11)) [2]
   a__U21(tt, s(V12)) -> a__U22(a__U21(a__isNatKind(V12), V12)) [2]
   a__U21(tt, V1) -> a__U22(isNat(V1)) [2]
   a__U22(tt) -> tt [1]
   a__U31(tt, nil) -> a__U32(tt) [2]
   a__U31(tt, cons(V13, V21)) -> a__U32(a__U51(a__and(a__isNatKind(V13), isNatIListKind(V21)), V13, V21)) [2]
   a__U31(tt, take(V14, V22)) -> a__U32(a__U61(a__and(a__isNatKind(V14), isNatIListKind(V22)), V14, V22)) [2]
   a__U31(tt, V) -> a__U32(isNatList(V)) [2]
   a__U32(tt) -> tt [1]
   a__U41(tt, 0, V2) -> a__U42(tt, V2) [2]
   a__U41(tt, length(V15), V2) -> a__U42(a__U11(a__isNatIListKind(V15), V15), V2) [2]
   a__U41(tt, s(V16), V2) -> a__U42(a__U21(a__isNatKind(V16), V16), V2) [2]
   a__U41(tt, V1, V2) -> a__U42(isNat(V1), V2) [2]
   a__U42(tt, V2) -> a__U43(a__U31(a__isNatIListKind(V2), V2)) [2]
   a__U42(tt, zeros) -> a__U43(tt) [2]
   a__U42(tt, cons(V17, V23)) -> a__U43(a__U41(a__and(a__isNatKind(V17), isNatIListKind(V23)), V17, V23)) [2]
   a__U42(tt, V2) -> a__U43(isNatIList(V2)) [2]
   a__U43(tt) -> tt [1]
   a__U51(tt, 0, V2) -> a__U52(tt, V2) [2]
   a__U51(tt, length(V18), V2) -> a__U52(a__U11(a__isNatIListKind(V18), V18), V2) [2]
   a__U51(tt, s(V19), V2) -> a__U52(a__U21(a__isNatKind(V19), V19), V2) [2]
   a__U51(tt, V1, V2) -> a__U52(isNat(V1), V2) [2]
   a__U52(tt, nil) -> a__U53(tt) [2]
   a__U52(tt, cons(V110, V24)) -> a__U53(a__U51(a__and(a__isNatKind(V110), isNatIListKind(V24)), V110, V24)) [2]
   a__U52(tt, take(V111, V25)) -> a__U53(a__U61(a__and(a__isNatKind(V111), isNatIListKind(V25)), V111, V25)) [2]
   a__U52(tt, V2) -> a__U53(isNatList(V2)) [2]
   a__U53(tt) -> tt [1]
   a__U61(tt, 0, V2) -> a__U62(tt, V2) [2]
   a__U61(tt, length(V112), V2) -> a__U62(a__U11(a__isNatIListKind(V112), V112), V2) [2]
   a__U61(tt, s(V113), V2) -> a__U62(a__U21(a__isNatKind(V113), V113), V2) [2]
   a__U61(tt, V1, V2) -> a__U62(isNat(V1), V2) [2]
   a__U62(tt, V2) -> a__U63(a__U31(a__isNatIListKind(V2), V2)) [2]
   a__U62(tt, zeros) -> a__U63(tt) [2]
   a__U62(tt, cons(V114, V26)) -> a__U63(a__U41(a__and(a__isNatKind(V114), isNatIListKind(V26)), V114, V26)) [2]
   a__U62(tt, V2) -> a__U63(isNatIList(V2)) [2]
   a__U63(tt) -> tt [1]
   a__U71(tt, L) -> s(a__length(mark(L))) [1]
   a__U81(tt) -> nil [1]
   a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1]
   a__and(tt, X) -> mark(X) [1]
   a__isNat(0) -> tt [1]
   a__isNat(length(nil)) -> a__U11(tt, nil) [2]
   a__isNat(length(zeros)) -> a__U11(tt, zeros) [2]
   a__isNat(length(cons(V115, V27))) -> a__U11(a__and(a__isNatKind(V115), isNatIListKind(V27)), cons(V115, V27)) [2]
   a__isNat(length(take(V116, V28))) -> a__U11(a__and(a__isNatKind(V116), isNatIListKind(V28)), take(V116, V28)) [2]
   a__isNat(length(V1)) -> a__U11(isNatIListKind(V1), V1) [2]
   a__isNat(s(0)) -> a__U21(tt, 0) [2]
   a__isNat(s(length(V117))) -> a__U21(a__isNatIListKind(V117), length(V117)) [2]
   a__isNat(s(s(V118))) -> a__U21(a__isNatKind(V118), s(V118)) [2]
   a__isNat(s(V1)) -> a__U21(isNatKind(V1), V1) [2]
   a__isNatIList(nil) -> a__U31(tt, nil) [2]
   a__isNatIList(zeros) -> a__U31(tt, zeros) [2]
   a__isNatIList(cons(V119, V29)) -> a__U31(a__and(a__isNatKind(V119), isNatIListKind(V29)), cons(V119, V29)) [2]
   a__isNatIList(take(V120, V210)) -> a__U31(a__and(a__isNatKind(V120), isNatIListKind(V210)), take(V120, V210)) [2]
   a__isNatIList(V) -> a__U31(isNatIListKind(V), V) [2]
   a__isNatIList(zeros) -> tt [1]
   a__isNatIList(cons(0, V2)) -> a__U41(a__and(tt, isNatIListKind(V2)), 0, V2) [2]
   a__isNatIList(cons(length(V121), V2)) -> a__U41(a__and(a__isNatIListKind(V121), isNatIListKind(V2)), length(V121), V2) [2]
   a__isNatIList(cons(s(V122), V2)) -> a__U41(a__and(a__isNatKind(V122), isNatIListKind(V2)), s(V122), V2) [2]
   a__isNatIList(cons(V1, V2)) -> a__U41(a__and(isNatKind(V1), isNatIListKind(V2)), V1, V2) [2]
   a__isNatIListKind(nil) -> tt [1]
   a__isNatIListKind(zeros) -> tt [1]
   a__isNatIListKind(cons(0, V2)) -> a__and(tt, isNatIListKind(V2)) [2]
   a__isNatIListKind(cons(length(V123), V2)) -> a__and(a__isNatIListKind(V123), isNatIListKind(V2)) [2]
   a__isNatIListKind(cons(s(V124), V2)) -> a__and(a__isNatKind(V124), isNatIListKind(V2)) [2]
   a__isNatIListKind(cons(V1, V2)) -> a__and(isNatKind(V1), isNatIListKind(V2)) [2]
   a__isNatIListKind(take(0, V2)) -> a__and(tt, isNatIListKind(V2)) [2]
   a__isNatIListKind(take(length(V125), V2)) -> a__and(a__isNatIListKind(V125), isNatIListKind(V2)) [2]
   a__isNatIListKind(take(s(V126), V2)) -> a__and(a__isNatKind(V126), isNatIListKind(V2)) [2]
   a__isNatIListKind(take(V1, V2)) -> a__and(isNatKind(V1), isNatIListKind(V2)) [2]
   a__isNatKind(0) -> tt [1]
   a__isNatKind(length(V1)) -> a__isNatIListKind(V1) [1]
   a__isNatKind(s(V1)) -> a__isNatKind(V1) [1]
   a__isNatList(nil) -> tt [1]
   a__isNatList(cons(0, V2)) -> a__U51(a__and(tt, isNatIListKind(V2)), 0, V2) [2]
   a__isNatList(cons(length(V127), V2)) -> a__U51(a__and(a__isNatIListKind(V127), isNatIListKind(V2)), length(V127), V2) [2]
   a__isNatList(cons(s(V128), V2)) -> a__U51(a__and(a__isNatKind(V128), isNatIListKind(V2)), s(V128), V2) [2]
   a__isNatList(cons(V1, V2)) -> a__U51(a__and(isNatKind(V1), isNatIListKind(V2)), V1, V2) [2]
   a__isNatList(take(0, V2)) -> a__U61(a__and(tt, isNatIListKind(V2)), 0, V2) [2]
   a__isNatList(take(length(V129), V2)) -> a__U61(a__and(a__isNatIListKind(V129), isNatIListKind(V2)), length(V129), V2) [2]
   a__isNatList(take(s(V130), V2)) -> a__U61(a__and(a__isNatKind(V130), isNatIListKind(V2)), s(V130), V2) [2]
   a__isNatList(take(V1, V2)) -> a__U61(a__and(isNatKind(V1), isNatIListKind(V2)), V1, V2) [2]
   a__length(nil) -> 0 [1]
   a__length(cons(N, nil)) -> a__U71(a__and(a__and(tt, isNatIListKind(nil)), and(isNat(N), isNatKind(N))), nil) [2]
   a__length(cons(N, cons(V131, V211))) -> a__U71(a__and(a__and(a__U51(a__and(a__isNatKind(V131), isNatIListKind(V211)), V131, V211), isNatIListKind(cons(V131, V211))), and(isNat(N), isNatKind(N))), cons(V131, V211)) [2]
   a__length(cons(N, take(V132, V212))) -> a__U71(a__and(a__and(a__U61(a__and(a__isNatKind(V132), isNatIListKind(V212)), V132, V212), isNatIListKind(take(V132, V212))), and(isNat(N), isNatKind(N))), take(V132, V212)) [2]
   a__length(cons(N, L)) -> a__U71(a__and(a__and(isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) [2]
   a__take(0, IL) -> a__U81(a__and(a__U31(a__isNatIListKind(IL), IL), isNatIListKind(IL))) [2]
   a__take(0, zeros) -> a__U81(a__and(tt, isNatIListKind(zeros))) [2]
   a__take(0, cons(V133, V213)) -> a__U81(a__and(a__U41(a__and(a__isNatKind(V133), isNatIListKind(V213)), V133, V213), isNatIListKind(cons(V133, V213)))) [2]
   a__take(0, IL) -> a__U81(a__and(isNatIList(IL), isNatIListKind(IL))) [2]
   a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__U31(a__isNatIListKind(IL), IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) [2]
   a__take(s(M), cons(N, zeros)) -> a__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), zeros, M, N) [2]
   a__take(s(M), cons(N, cons(V134, V214))) -> a__U91(a__and(a__and(a__U41(a__and(a__isNatKind(V134), isNatIListKind(V214)), V134, V214), isNatIListKind(cons(V134, V214))), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), cons(V134, V214), M, N) [2]
   a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) [2]
   mark(zeros) -> a__zeros [1]
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1]
   mark(U12(X)) -> a__U12(mark(X)) [1]
   mark(isNatList(X)) -> a__isNatList(X) [1]
   mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1]
   mark(U22(X)) -> a__U22(mark(X)) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1]
   mark(U32(X)) -> a__U32(mark(X)) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(U42(X1, X2)) -> a__U42(mark(X1), X2) [1]
   mark(U43(X)) -> a__U43(mark(X)) [1]
   mark(isNatIList(X)) -> a__isNatIList(X) [1]
   mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) [1]
   mark(U52(X1, X2)) -> a__U52(mark(X1), X2) [1]
   mark(U53(X)) -> a__U53(mark(X)) [1]
   mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) [1]
   mark(U62(X1, X2)) -> a__U62(mark(X1), X2) [1]
   mark(U63(X)) -> a__U63(mark(X)) [1]
   mark(U71(X1, X2)) -> a__U71(mark(X1), X2) [1]
   mark(length(X)) -> a__length(mark(X)) [1]
   mark(U81(X)) -> a__U81(mark(X)) [1]
   mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) [1]
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), X2) [1]
   mark(isNatIListKind(X)) -> a__isNatIListKind(X) [1]
   mark(isNatKind(X)) -> a__isNatKind(X) [1]
   mark(cons(X1, X2)) -> cons(mark(X1), X2) [1]
   mark(0) -> 0 [1]
   mark(tt) -> tt [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(nil) -> nil [1]
   a__zeros -> zeros [1]
   a__U11(X1, X2) -> U11(X1, X2) [1]
   a__U12(X) -> U12(X) [1]
   a__isNatList(X) -> isNatList(X) [1]
   a__U21(X1, X2) -> U21(X1, X2) [1]
   a__U22(X) -> U22(X) [1]
   a__isNat(X) -> isNat(X) [1]
   a__U31(X1, X2) -> U31(X1, X2) [1]
   a__U32(X) -> U32(X) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__U42(X1, X2) -> U42(X1, X2) [1]
   a__U43(X) -> U43(X) [1]
   a__isNatIList(X) -> isNatIList(X) [1]
   a__U51(X1, X2, X3) -> U51(X1, X2, X3) [1]
   a__U52(X1, X2) -> U52(X1, X2) [1]
   a__U53(X) -> U53(X) [1]
   a__U61(X1, X2, X3) -> U61(X1, X2, X3) [1]
   a__U62(X1, X2) -> U62(X1, X2) [1]
   a__U63(X) -> U63(X) [1]
   a__U71(X1, X2) -> U71(X1, X2) [1]
   a__length(X) -> length(X) [1]
   a__U81(X) -> U81(X) [1]
   a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) [1]
   a__take(X1, X2) -> take(X1, X2) [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNatIListKind(X) -> isNatIListKind(X) [1]
   a__isNatKind(X) -> isNatKind(X) [1]

The TRS has the following type information:
a__zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
cons :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
0 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
tt :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
s :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
mark :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
nil :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91

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

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

   0 => 0
   zeros => 3
   tt => 2
   nil => 1

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

(14)
Obligation:
Complexity RNTS consisting of the following rules:

   a__U11(z, z') -{ 2 }-> a__U12(a__U61(a__and(a__isNatKind(V1''), 1 + V2''), V1'', V2'')) :|: z = 2, V1'' >= 0, V2'' >= 0, z' = 1 + V1'' + V2''
   a__U11(z, z') -{ 2 }-> a__U12(a__U51(a__and(a__isNatKind(V1'), 1 + V2'), V1', V2')) :|: z = 2, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0
   a__U11(z, z') -{ 2 }-> a__U12(2) :|: z = 2, z' = 1
   a__U11(z, z') -{ 2 }-> a__U12(1 + V1) :|: z = 2, V1 >= 0, z' = V1
   a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U12(z) -{ 1 }-> 2 :|: z = 2
   a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U21(z, z') -{ 2 }-> a__U22(a__U21(a__isNatKind(V12), V12)) :|: z = 2, V12 >= 0, z' = 1 + V12
   a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__isNatIListKind(V11), V11)) :|: z = 2, V11 >= 0, z' = 1 + V11
   a__U21(z, z') -{ 2 }-> a__U22(2) :|: z = 2, z' = 0
   a__U21(z, z') -{ 2 }-> a__U22(1 + V1) :|: z = 2, V1 >= 0, z' = V1
   a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U22(z) -{ 1 }-> 2 :|: z = 2
   a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U31(z, z') -{ 2 }-> a__U32(a__U61(a__and(a__isNatKind(V14), 1 + V22), V14, V22)) :|: z = 2, V14 >= 0, z' = 1 + V14 + V22, V22 >= 0
   a__U31(z, z') -{ 2 }-> a__U32(a__U51(a__and(a__isNatKind(V13), 1 + V21), V13, V21)) :|: z = 2, V21 >= 0, V13 >= 0, z' = 1 + V13 + V21
   a__U31(z, z') -{ 2 }-> a__U32(2) :|: z = 2, z' = 1
   a__U31(z, z') -{ 2 }-> a__U32(1 + V) :|: z = 2, z' = V, V >= 0
   a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U32(z) -{ 1 }-> 2 :|: z = 2
   a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U41(z, z', z'') -{ 2 }-> a__U42(a__U21(a__isNatKind(V16), V16), V2) :|: z = 2, z' = 1 + V16, V16 >= 0, V2 >= 0, z'' = V2
   a__U41(z, z', z'') -{ 2 }-> a__U42(a__U11(a__isNatIListKind(V15), V15), V2) :|: z = 2, z' = 1 + V15, V2 >= 0, V15 >= 0, z'' = V2
   a__U41(z, z', z'') -{ 2 }-> a__U42(2, V2) :|: z = 2, V2 >= 0, z'' = V2, z' = 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(1 + V1, V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1
   a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U42(z, z') -{ 2 }-> a__U43(a__U41(a__and(a__isNatKind(V17), 1 + V23), V17, V23)) :|: z = 2, z' = 1 + V17 + V23, V23 >= 0, V17 >= 0
   a__U42(z, z') -{ 2 }-> a__U43(a__U31(a__isNatIListKind(V2), V2)) :|: z = 2, z' = V2, V2 >= 0
   a__U42(z, z') -{ 2 }-> a__U43(2) :|: z = 2, z' = 3
   a__U42(z, z') -{ 2 }-> a__U43(1 + V2) :|: z = 2, z' = V2, V2 >= 0
   a__U42(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U43(z) -{ 1 }-> 2 :|: z = 2
   a__U43(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U51(z, z', z'') -{ 2 }-> a__U52(a__U21(a__isNatKind(V19), V19), V2) :|: z = 2, z' = 1 + V19, V19 >= 0, V2 >= 0, z'' = V2
   a__U51(z, z', z'') -{ 2 }-> a__U52(a__U11(a__isNatIListKind(V18), V18), V2) :|: z = 2, V18 >= 0, z' = 1 + V18, V2 >= 0, z'' = V2
   a__U51(z, z', z'') -{ 2 }-> a__U52(2, V2) :|: z = 2, V2 >= 0, z'' = V2, z' = 0
   a__U51(z, z', z'') -{ 2 }-> a__U52(1 + V1, V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1
   a__U51(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U52(z, z') -{ 2 }-> a__U53(a__U61(a__and(a__isNatKind(V111), 1 + V25), V111, V25)) :|: z = 2, V25 >= 0, z' = 1 + V111 + V25, V111 >= 0
   a__U52(z, z') -{ 2 }-> a__U53(a__U51(a__and(a__isNatKind(V110), 1 + V24), V110, V24)) :|: z = 2, V110 >= 0, V24 >= 0, z' = 1 + V110 + V24
   a__U52(z, z') -{ 2 }-> a__U53(2) :|: z = 2, z' = 1
   a__U52(z, z') -{ 2 }-> a__U53(1 + V2) :|: z = 2, z' = V2, V2 >= 0
   a__U52(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U53(z) -{ 1 }-> 2 :|: z = 2
   a__U53(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U61(z, z', z'') -{ 2 }-> a__U62(a__U21(a__isNatKind(V113), V113), V2) :|: z = 2, V2 >= 0, z' = 1 + V113, z'' = V2, V113 >= 0
   a__U61(z, z', z'') -{ 2 }-> a__U62(a__U11(a__isNatIListKind(V112), V112), V2) :|: z = 2, V2 >= 0, V112 >= 0, z' = 1 + V112, z'' = V2
   a__U61(z, z', z'') -{ 2 }-> a__U62(2, V2) :|: z = 2, V2 >= 0, z'' = V2, z' = 0
   a__U61(z, z', z'') -{ 2 }-> a__U62(1 + V1, V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1
   a__U61(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U62(z, z') -{ 2 }-> a__U63(a__U41(a__and(a__isNatKind(V114), 1 + V26), V114, V26)) :|: z = 2, z' = 1 + V114 + V26, V114 >= 0, V26 >= 0
   a__U62(z, z') -{ 2 }-> a__U63(a__U31(a__isNatIListKind(V2), V2)) :|: z = 2, z' = V2, V2 >= 0
   a__U62(z, z') -{ 2 }-> a__U63(2) :|: z = 2, z' = 3
   a__U62(z, z') -{ 2 }-> a__U63(1 + V2) :|: z = 2, z' = V2, V2 >= 0
   a__U62(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U63(z) -{ 1 }-> 2 :|: z = 2
   a__U63(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U71(z, z') -{ 1 }-> 1 + a__length(mark(L)) :|: z = 2, L >= 0, z' = L
   a__U71(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U81(z) -{ 1 }-> 1 :|: z = 2
   a__U81(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U91(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0
   a__U91(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3
   a__and(z, z') -{ 1 }-> mark(X) :|: z = 2, z' = X, X >= 0
   a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__isNat(z) -{ 2 }-> a__U21(a__isNatKind(V118), 1 + V118) :|: V118 >= 0, z = 1 + (1 + V118)
   a__isNat(z) -{ 2 }-> a__U21(a__isNatIListKind(V117), 1 + V117) :|: V117 >= 0, z = 1 + (1 + V117)
   a__isNat(z) -{ 2 }-> a__U21(2, 0) :|: z = 1 + 0
   a__isNat(z) -{ 2 }-> a__U21(1 + V1, V1) :|: z = 1 + V1, V1 >= 0
   a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V115), 1 + V27), 1 + V115 + V27) :|: z = 1 + (1 + V115 + V27), V115 >= 0, V27 >= 0
   a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V116), 1 + V28), 1 + V116 + V28) :|: V28 >= 0, z = 1 + (1 + V116 + V28), V116 >= 0
   a__isNat(z) -{ 2 }-> a__U11(2, 3) :|: z = 1 + 3
   a__isNat(z) -{ 2 }-> a__U11(2, 1) :|: z = 1 + 1
   a__isNat(z) -{ 2 }-> a__U11(1 + V1, V1) :|: z = 1 + V1, V1 >= 0
   a__isNat(z) -{ 1 }-> 2 :|: z = 0
   a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatIList(z) -{ 2 }-> a__U41(a__and(a__isNatKind(V122), 1 + V2), 1 + V122, V2) :|: z = 1 + (1 + V122) + V2, V2 >= 0, V122 >= 0
   a__isNatIList(z) -{ 2 }-> a__U41(a__and(a__isNatIListKind(V121), 1 + V2), 1 + V121, V2) :|: V121 >= 0, z = 1 + (1 + V121) + V2, V2 >= 0
   a__isNatIList(z) -{ 2 }-> a__U41(a__and(2, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNatIList(z) -{ 2 }-> a__U41(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatIList(z) -{ 2 }-> a__U31(a__and(a__isNatKind(V119), 1 + V29), 1 + V119 + V29) :|: V29 >= 0, z = 1 + V119 + V29, V119 >= 0
   a__isNatIList(z) -{ 2 }-> a__U31(a__and(a__isNatKind(V120), 1 + V210), 1 + V120 + V210) :|: V120 >= 0, z = 1 + V120 + V210, V210 >= 0
   a__isNatIList(z) -{ 2 }-> a__U31(2, 3) :|: z = 3
   a__isNatIList(z) -{ 2 }-> a__U31(2, 1) :|: z = 1
   a__isNatIList(z) -{ 2 }-> a__U31(1 + V, V) :|: z = V, V >= 0
   a__isNatIList(z) -{ 1 }-> 2 :|: z = 3
   a__isNatIList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatKind(V124), 1 + V2) :|: V124 >= 0, V2 >= 0, z = 1 + (1 + V124) + V2
   a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatKind(V126), 1 + V2) :|: V2 >= 0, V126 >= 0, z = 1 + (1 + V126) + V2
   a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatIListKind(V123), 1 + V2) :|: V2 >= 0, z = 1 + (1 + V123) + V2, V123 >= 0
   a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatIListKind(V125), 1 + V2) :|: V125 >= 0, z = 1 + (1 + V125) + V2, V2 >= 0
   a__isNatIListKind(z) -{ 2 }-> a__and(2, 1 + V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNatIListKind(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 1
   a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 3
   a__isNatIListKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatKind(z) -{ 1 }-> a__isNatKind(V1) :|: z = 1 + V1, V1 >= 0
   a__isNatKind(z) -{ 1 }-> a__isNatIListKind(V1) :|: z = 1 + V1, V1 >= 0
   a__isNatKind(z) -{ 1 }-> 2 :|: z = 0
   a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatList(z) -{ 2 }-> a__U61(a__and(a__isNatKind(V130), 1 + V2), 1 + V130, V2) :|: z = 1 + (1 + V130) + V2, V130 >= 0, V2 >= 0
   a__isNatList(z) -{ 2 }-> a__U61(a__and(a__isNatIListKind(V129), 1 + V2), 1 + V129, V2) :|: z = 1 + (1 + V129) + V2, V2 >= 0, V129 >= 0
   a__isNatList(z) -{ 2 }-> a__U61(a__and(2, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNatList(z) -{ 2 }-> a__U61(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatList(z) -{ 2 }-> a__U51(a__and(a__isNatKind(V128), 1 + V2), 1 + V128, V2) :|: V128 >= 0, V2 >= 0, z = 1 + (1 + V128) + V2
   a__isNatList(z) -{ 2 }-> a__U51(a__and(a__isNatIListKind(V127), 1 + V2), 1 + V127, V2) :|: V127 >= 0, V2 >= 0, z = 1 + (1 + V127) + V2
   a__isNatList(z) -{ 2 }-> a__U51(a__and(2, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNatList(z) -{ 2 }-> a__U51(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatList(z) -{ 1 }-> 2 :|: z = 1
   a__isNatList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__length(z) -{ 2 }-> a__U71(a__and(a__and(a__U61(a__and(a__isNatKind(V132), 1 + V212), V132, V212), 1 + (1 + V132 + V212)), 1 + (1 + N) + (1 + N)), 1 + V132 + V212) :|: z = 1 + N + (1 + V132 + V212), V132 >= 0, N >= 0, V212 >= 0
   a__length(z) -{ 2 }-> a__U71(a__and(a__and(a__U51(a__and(a__isNatKind(V131), 1 + V211), V131, V211), 1 + (1 + V131 + V211)), 1 + (1 + N) + (1 + N)), 1 + V131 + V211) :|: V131 >= 0, z = 1 + N + (1 + V131 + V211), V211 >= 0, N >= 0
   a__length(z) -{ 2 }-> a__U71(a__and(a__and(2, 1 + 1), 1 + (1 + N) + (1 + N)), 1) :|: z = 1 + N + 1, N >= 0
   a__length(z) -{ 2 }-> a__U71(a__and(a__and(1 + L, 1 + L), 1 + (1 + N) + (1 + N)), L) :|: z = 1 + N + L, L >= 0, N >= 0
   a__length(z) -{ 1 }-> 0 :|: z = 1
   a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(a__U41(a__and(a__isNatKind(V134), 1 + V214), V134, V214), 1 + (1 + V134 + V214)), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), 1 + V134 + V214, M, N) :|: z = 1 + M, V214 >= 0, z' = 1 + N + (1 + V134 + V214), M >= 0, V134 >= 0, N >= 0
   a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(a__U31(a__isNatIListKind(IL), IL), 1 + IL), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0
   a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(2, 1 + 3), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), 3, M, N) :|: z = 1 + M, M >= 0, z' = 1 + N + 3, N >= 0
   a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(1 + IL, 1 + IL), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0
   a__take(z, z') -{ 2 }-> a__U81(a__and(a__U41(a__and(a__isNatKind(V133), 1 + V213), V133, V213), 1 + (1 + V133 + V213))) :|: V213 >= 0, z' = 1 + V133 + V213, z = 0, V133 >= 0
   a__take(z, z') -{ 2 }-> a__U81(a__and(a__U31(a__isNatIListKind(IL), IL), 1 + IL)) :|: z' = IL, z = 0, IL >= 0
   a__take(z, z') -{ 2 }-> a__U81(a__and(2, 1 + 3)) :|: z' = 3, z = 0
   a__take(z, z') -{ 2 }-> a__U81(a__and(1 + IL, 1 + IL)) :|: z' = IL, z = 0, IL >= 0
   a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__zeros -{ 1 }-> 3 :|: 
   a__zeros -{ 1 }-> 1 + 0 + 3 :|: 
   mark(z) -{ 1 }-> a__zeros :|: z = 3
   mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__length(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatList(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatIListKind(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatIList(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__and(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U91(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 1 }-> a__U81(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U71(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U63(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U62(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U61(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U53(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U52(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U51(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U43(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U42(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U41(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U32(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U22(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U21(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U12(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U11(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> 2 :|: z = 2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2


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

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

   a__zeros -{ 1 }-> 3 :|: 
   a__zeros -{ 1 }-> 1 + 0 + 3 :|: 
   a__U12(z) -{ 1 }-> 2 :|: z = 2
   a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U22(z) -{ 1 }-> 2 :|: z = 2
   a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U32(z) -{ 1 }-> 2 :|: z = 2
   a__U43(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U43(z) -{ 1 }-> 2 :|: z = 2
   a__U53(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U53(z) -{ 1 }-> 2 :|: z = 2
   a__U63(z) -{ 1 }-> 2 :|: z = 2
   a__U63(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U81(z) -{ 1 }-> 1 :|: z = 2
   a__U81(z) -{ 1 }-> 1 + X :|: X >= 0, z = X

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

(16)
Obligation:
Complexity RNTS consisting of the following rules:

   a__U11(z, z') -{ 2 }-> a__U12(a__U61(a__and(a__isNatKind(V1''), 1 + V2''), V1'', V2'')) :|: z = 2, V1'' >= 0, V2'' >= 0, z' = 1 + V1'' + V2''
   a__U11(z, z') -{ 2 }-> a__U12(a__U51(a__and(a__isNatKind(V1'), 1 + V2'), V1', V2')) :|: z = 2, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0
   a__U11(z, z') -{ 3 }-> 2 :|: z = 2, z' = 1, 2 = 2
   a__U11(z, z') -{ 3 }-> 2 :|: z = 2, V1 >= 0, z' = V1, 1 + V1 = 2
   a__U11(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 1, X >= 0, 2 = X
   a__U11(z, z') -{ 3 }-> 1 + X :|: z = 2, V1 >= 0, z' = V1, X >= 0, 1 + V1 = X
   a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U12(z) -{ 1 }-> 2 :|: z = 2
   a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U21(z, z') -{ 2 }-> a__U22(a__U21(a__isNatKind(V12), V12)) :|: z = 2, V12 >= 0, z' = 1 + V12
   a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__isNatIListKind(V11), V11)) :|: z = 2, V11 >= 0, z' = 1 + V11
   a__U21(z, z') -{ 3 }-> 2 :|: z = 2, z' = 0, 2 = 2
   a__U21(z, z') -{ 3 }-> 2 :|: z = 2, V1 >= 0, z' = V1, 1 + V1 = 2
   a__U21(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 0, X >= 0, 2 = X
   a__U21(z, z') -{ 3 }-> 1 + X :|: z = 2, V1 >= 0, z' = V1, X >= 0, 1 + V1 = X
   a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U22(z) -{ 1 }-> 2 :|: z = 2
   a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U31(z, z') -{ 2 }-> a__U32(a__U61(a__and(a__isNatKind(V14), 1 + V22), V14, V22)) :|: z = 2, V14 >= 0, z' = 1 + V14 + V22, V22 >= 0
   a__U31(z, z') -{ 2 }-> a__U32(a__U51(a__and(a__isNatKind(V13), 1 + V21), V13, V21)) :|: z = 2, V21 >= 0, V13 >= 0, z' = 1 + V13 + V21
   a__U31(z, z') -{ 3 }-> 2 :|: z = 2, z' = 1, 2 = 2
   a__U31(z, z') -{ 3 }-> 2 :|: z = 2, z' = V, V >= 0, 1 + V = 2
   a__U31(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 1, X >= 0, 2 = X
   a__U31(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = V, V >= 0, X >= 0, 1 + V = X
   a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U32(z) -{ 1 }-> 2 :|: z = 2
   a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U41(z, z', z'') -{ 2 }-> a__U42(a__U21(a__isNatKind(V16), V16), V2) :|: z = 2, z' = 1 + V16, V16 >= 0, V2 >= 0, z'' = V2
   a__U41(z, z', z'') -{ 2 }-> a__U42(a__U11(a__isNatIListKind(V15), V15), V2) :|: z = 2, z' = 1 + V15, V2 >= 0, V15 >= 0, z'' = V2
   a__U41(z, z', z'') -{ 2 }-> a__U42(2, V2) :|: z = 2, V2 >= 0, z'' = V2, z' = 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(1 + V1, V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1
   a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U42(z, z') -{ 2 }-> a__U43(a__U41(a__and(a__isNatKind(V17), 1 + V23), V17, V23)) :|: z = 2, z' = 1 + V17 + V23, V23 >= 0, V17 >= 0
   a__U42(z, z') -{ 2 }-> a__U43(a__U31(a__isNatIListKind(V2), V2)) :|: z = 2, z' = V2, V2 >= 0
   a__U42(z, z') -{ 3 }-> 2 :|: z = 2, z' = 3, 2 = 2
   a__U42(z, z') -{ 3 }-> 2 :|: z = 2, z' = V2, V2 >= 0, 1 + V2 = 2
   a__U42(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 3, X >= 0, 2 = X
   a__U42(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = V2, V2 >= 0, X >= 0, 1 + V2 = X
   a__U42(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U43(z) -{ 1 }-> 2 :|: z = 2
   a__U43(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U51(z, z', z'') -{ 2 }-> a__U52(a__U21(a__isNatKind(V19), V19), V2) :|: z = 2, z' = 1 + V19, V19 >= 0, V2 >= 0, z'' = V2
   a__U51(z, z', z'') -{ 2 }-> a__U52(a__U11(a__isNatIListKind(V18), V18), V2) :|: z = 2, V18 >= 0, z' = 1 + V18, V2 >= 0, z'' = V2
   a__U51(z, z', z'') -{ 2 }-> a__U52(2, V2) :|: z = 2, V2 >= 0, z'' = V2, z' = 0
   a__U51(z, z', z'') -{ 2 }-> a__U52(1 + V1, V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1
   a__U51(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U52(z, z') -{ 2 }-> a__U53(a__U61(a__and(a__isNatKind(V111), 1 + V25), V111, V25)) :|: z = 2, V25 >= 0, z' = 1 + V111 + V25, V111 >= 0
   a__U52(z, z') -{ 2 }-> a__U53(a__U51(a__and(a__isNatKind(V110), 1 + V24), V110, V24)) :|: z = 2, V110 >= 0, V24 >= 0, z' = 1 + V110 + V24
   a__U52(z, z') -{ 3 }-> 2 :|: z = 2, z' = 1, 2 = 2
   a__U52(z, z') -{ 3 }-> 2 :|: z = 2, z' = V2, V2 >= 0, 1 + V2 = 2
   a__U52(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 1, X >= 0, 2 = X
   a__U52(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = V2, V2 >= 0, X >= 0, 1 + V2 = X
   a__U52(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U53(z) -{ 1 }-> 2 :|: z = 2
   a__U53(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U61(z, z', z'') -{ 2 }-> a__U62(a__U21(a__isNatKind(V113), V113), V2) :|: z = 2, V2 >= 0, z' = 1 + V113, z'' = V2, V113 >= 0
   a__U61(z, z', z'') -{ 2 }-> a__U62(a__U11(a__isNatIListKind(V112), V112), V2) :|: z = 2, V2 >= 0, V112 >= 0, z' = 1 + V112, z'' = V2
   a__U61(z, z', z'') -{ 2 }-> a__U62(2, V2) :|: z = 2, V2 >= 0, z'' = V2, z' = 0
   a__U61(z, z', z'') -{ 2 }-> a__U62(1 + V1, V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1
   a__U61(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U62(z, z') -{ 2 }-> a__U63(a__U41(a__and(a__isNatKind(V114), 1 + V26), V114, V26)) :|: z = 2, z' = 1 + V114 + V26, V114 >= 0, V26 >= 0
   a__U62(z, z') -{ 2 }-> a__U63(a__U31(a__isNatIListKind(V2), V2)) :|: z = 2, z' = V2, V2 >= 0
   a__U62(z, z') -{ 3 }-> 2 :|: z = 2, z' = 3, 2 = 2
   a__U62(z, z') -{ 3 }-> 2 :|: z = 2, z' = V2, V2 >= 0, 1 + V2 = 2
   a__U62(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 3, X >= 0, 2 = X
   a__U62(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = V2, V2 >= 0, X >= 0, 1 + V2 = X
   a__U62(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U63(z) -{ 1 }-> 2 :|: z = 2
   a__U63(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U71(z, z') -{ 1 }-> 1 + a__length(mark(L)) :|: z = 2, L >= 0, z' = L
   a__U71(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U81(z) -{ 1 }-> 1 :|: z = 2
   a__U81(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U91(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0
   a__U91(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3
   a__and(z, z') -{ 1 }-> mark(X) :|: z = 2, z' = X, X >= 0
   a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__isNat(z) -{ 2 }-> a__U21(a__isNatKind(V118), 1 + V118) :|: V118 >= 0, z = 1 + (1 + V118)
   a__isNat(z) -{ 2 }-> a__U21(a__isNatIListKind(V117), 1 + V117) :|: V117 >= 0, z = 1 + (1 + V117)
   a__isNat(z) -{ 2 }-> a__U21(2, 0) :|: z = 1 + 0
   a__isNat(z) -{ 2 }-> a__U21(1 + V1, V1) :|: z = 1 + V1, V1 >= 0
   a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V115), 1 + V27), 1 + V115 + V27) :|: z = 1 + (1 + V115 + V27), V115 >= 0, V27 >= 0
   a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V116), 1 + V28), 1 + V116 + V28) :|: V28 >= 0, z = 1 + (1 + V116 + V28), V116 >= 0
   a__isNat(z) -{ 2 }-> a__U11(2, 3) :|: z = 1 + 3
   a__isNat(z) -{ 2 }-> a__U11(2, 1) :|: z = 1 + 1
   a__isNat(z) -{ 2 }-> a__U11(1 + V1, V1) :|: z = 1 + V1, V1 >= 0
   a__isNat(z) -{ 1 }-> 2 :|: z = 0
   a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatIList(z) -{ 2 }-> a__U41(a__and(a__isNatKind(V122), 1 + V2), 1 + V122, V2) :|: z = 1 + (1 + V122) + V2, V2 >= 0, V122 >= 0
   a__isNatIList(z) -{ 2 }-> a__U41(a__and(a__isNatIListKind(V121), 1 + V2), 1 + V121, V2) :|: V121 >= 0, z = 1 + (1 + V121) + V2, V2 >= 0
   a__isNatIList(z) -{ 2 }-> a__U41(a__and(2, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNatIList(z) -{ 2 }-> a__U41(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatIList(z) -{ 2 }-> a__U31(a__and(a__isNatKind(V119), 1 + V29), 1 + V119 + V29) :|: V29 >= 0, z = 1 + V119 + V29, V119 >= 0
   a__isNatIList(z) -{ 2 }-> a__U31(a__and(a__isNatKind(V120), 1 + V210), 1 + V120 + V210) :|: V120 >= 0, z = 1 + V120 + V210, V210 >= 0
   a__isNatIList(z) -{ 2 }-> a__U31(2, 3) :|: z = 3
   a__isNatIList(z) -{ 2 }-> a__U31(2, 1) :|: z = 1
   a__isNatIList(z) -{ 2 }-> a__U31(1 + V, V) :|: z = V, V >= 0
   a__isNatIList(z) -{ 1 }-> 2 :|: z = 3
   a__isNatIList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatKind(V124), 1 + V2) :|: V124 >= 0, V2 >= 0, z = 1 + (1 + V124) + V2
   a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatKind(V126), 1 + V2) :|: V2 >= 0, V126 >= 0, z = 1 + (1 + V126) + V2
   a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatIListKind(V123), 1 + V2) :|: V2 >= 0, z = 1 + (1 + V123) + V2, V123 >= 0
   a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatIListKind(V125), 1 + V2) :|: V125 >= 0, z = 1 + (1 + V125) + V2, V2 >= 0
   a__isNatIListKind(z) -{ 2 }-> a__and(2, 1 + V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNatIListKind(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 1
   a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 3
   a__isNatIListKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatKind(z) -{ 1 }-> a__isNatKind(V1) :|: z = 1 + V1, V1 >= 0
   a__isNatKind(z) -{ 1 }-> a__isNatIListKind(V1) :|: z = 1 + V1, V1 >= 0
   a__isNatKind(z) -{ 1 }-> 2 :|: z = 0
   a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatList(z) -{ 2 }-> a__U61(a__and(a__isNatKind(V130), 1 + V2), 1 + V130, V2) :|: z = 1 + (1 + V130) + V2, V130 >= 0, V2 >= 0
   a__isNatList(z) -{ 2 }-> a__U61(a__and(a__isNatIListKind(V129), 1 + V2), 1 + V129, V2) :|: z = 1 + (1 + V129) + V2, V2 >= 0, V129 >= 0
   a__isNatList(z) -{ 2 }-> a__U61(a__and(2, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNatList(z) -{ 2 }-> a__U61(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatList(z) -{ 2 }-> a__U51(a__and(a__isNatKind(V128), 1 + V2), 1 + V128, V2) :|: V128 >= 0, V2 >= 0, z = 1 + (1 + V128) + V2
   a__isNatList(z) -{ 2 }-> a__U51(a__and(a__isNatIListKind(V127), 1 + V2), 1 + V127, V2) :|: V127 >= 0, V2 >= 0, z = 1 + (1 + V127) + V2
   a__isNatList(z) -{ 2 }-> a__U51(a__and(2, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNatList(z) -{ 2 }-> a__U51(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatList(z) -{ 1 }-> 2 :|: z = 1
   a__isNatList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__length(z) -{ 2 }-> a__U71(a__and(a__and(a__U61(a__and(a__isNatKind(V132), 1 + V212), V132, V212), 1 + (1 + V132 + V212)), 1 + (1 + N) + (1 + N)), 1 + V132 + V212) :|: z = 1 + N + (1 + V132 + V212), V132 >= 0, N >= 0, V212 >= 0
   a__length(z) -{ 2 }-> a__U71(a__and(a__and(a__U51(a__and(a__isNatKind(V131), 1 + V211), V131, V211), 1 + (1 + V131 + V211)), 1 + (1 + N) + (1 + N)), 1 + V131 + V211) :|: V131 >= 0, z = 1 + N + (1 + V131 + V211), V211 >= 0, N >= 0
   a__length(z) -{ 2 }-> a__U71(a__and(a__and(2, 1 + 1), 1 + (1 + N) + (1 + N)), 1) :|: z = 1 + N + 1, N >= 0
   a__length(z) -{ 2 }-> a__U71(a__and(a__and(1 + L, 1 + L), 1 + (1 + N) + (1 + N)), L) :|: z = 1 + N + L, L >= 0, N >= 0
   a__length(z) -{ 1 }-> 0 :|: z = 1
   a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(a__U41(a__and(a__isNatKind(V134), 1 + V214), V134, V214), 1 + (1 + V134 + V214)), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), 1 + V134 + V214, M, N) :|: z = 1 + M, V214 >= 0, z' = 1 + N + (1 + V134 + V214), M >= 0, V134 >= 0, N >= 0
   a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(a__U31(a__isNatIListKind(IL), IL), 1 + IL), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0
   a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(2, 1 + 3), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), 3, M, N) :|: z = 1 + M, M >= 0, z' = 1 + N + 3, N >= 0
   a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(1 + IL, 1 + IL), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0
   a__take(z, z') -{ 2 }-> a__U81(a__and(a__U41(a__and(a__isNatKind(V133), 1 + V213), V133, V213), 1 + (1 + V133 + V213))) :|: V213 >= 0, z' = 1 + V133 + V213, z = 0, V133 >= 0
   a__take(z, z') -{ 2 }-> a__U81(a__and(a__U31(a__isNatIListKind(IL), IL), 1 + IL)) :|: z' = IL, z = 0, IL >= 0
   a__take(z, z') -{ 2 }-> a__U81(a__and(2, 1 + 3)) :|: z' = 3, z = 0
   a__take(z, z') -{ 2 }-> a__U81(a__and(1 + IL, 1 + IL)) :|: z' = IL, z = 0, IL >= 0
   a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__zeros -{ 1 }-> 3 :|: 
   a__zeros -{ 1 }-> 1 + 0 + 3 :|: 
   mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__length(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatList(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatIListKind(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatIList(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__and(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U91(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 1 }-> a__U81(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U71(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U63(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U62(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U61(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U53(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U52(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U51(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U43(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U42(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U41(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U32(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U22(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U21(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U12(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U11(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 2 }-> 3 :|: z = 3
   mark(z) -{ 1 }-> 2 :|: z = 2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 2 }-> 1 + 0 + 3 :|: z = 3


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

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

(18)
Obligation:
Complexity RNTS consisting of the following rules:

   a__U11(z, z') -{ 2 }-> a__U12(a__U61(a__and(a__isNatKind(V1''), 1 + V2''), V1'', V2'')) :|: z = 2, V1'' >= 0, V2'' >= 0, z' = 1 + V1'' + V2''
   a__U11(z, z') -{ 2 }-> a__U12(a__U51(a__and(a__isNatKind(V1'), 1 + V2'), V1', V2')) :|: z = 2, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0
   a__U11(z, z') -{ 3 }-> 2 :|: z = 2, z' = 1, 2 = 2
   a__U11(z, z') -{ 3 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2
   a__U11(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 1, X >= 0, 2 = X
   a__U11(z, z') -{ 3 }-> 1 + X :|: z = 2, z' >= 0, X >= 0, 1 + z' = X
   a__U11(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__U12(z) -{ 1 }-> 2 :|: z = 2
   a__U12(z) -{ 1 }-> 1 + z :|: z >= 0
   a__U21(z, z') -{ 2 }-> a__U22(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z = 2, z' - 1 >= 0
   a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__isNatIListKind(z' - 1), z' - 1)) :|: z = 2, z' - 1 >= 0
   a__U21(z, z') -{ 3 }-> 2 :|: z = 2, z' = 0, 2 = 2
   a__U21(z, z') -{ 3 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2
   a__U21(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 0, X >= 0, 2 = X
   a__U21(z, z') -{ 3 }-> 1 + X :|: z = 2, z' >= 0, X >= 0, 1 + z' = X
   a__U21(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__U22(z) -{ 1 }-> 2 :|: z = 2
   a__U22(z) -{ 1 }-> 1 + z :|: z >= 0
   a__U31(z, z') -{ 2 }-> a__U32(a__U61(a__and(a__isNatKind(V14), 1 + V22), V14, V22)) :|: z = 2, V14 >= 0, z' = 1 + V14 + V22, V22 >= 0
   a__U31(z, z') -{ 2 }-> a__U32(a__U51(a__and(a__isNatKind(V13), 1 + V21), V13, V21)) :|: z = 2, V21 >= 0, V13 >= 0, z' = 1 + V13 + V21
   a__U31(z, z') -{ 3 }-> 2 :|: z = 2, z' = 1, 2 = 2
   a__U31(z, z') -{ 3 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2
   a__U31(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 1, X >= 0, 2 = X
   a__U31(z, z') -{ 3 }-> 1 + X :|: z = 2, z' >= 0, X >= 0, 1 + z' = X
   a__U31(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__U32(z) -{ 1 }-> 2 :|: z = 2
   a__U32(z) -{ 1 }-> 1 + z :|: z >= 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(2, z'') :|: z = 2, z'' >= 0, z' = 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(1 + z', z'') :|: z = 2, z' >= 0, z'' >= 0
   a__U41(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0
   a__U42(z, z') -{ 2 }-> a__U43(a__U41(a__and(a__isNatKind(V17), 1 + V23), V17, V23)) :|: z = 2, z' = 1 + V17 + V23, V23 >= 0, V17 >= 0
   a__U42(z, z') -{ 2 }-> a__U43(a__U31(a__isNatIListKind(z'), z')) :|: z = 2, z' >= 0
   a__U42(z, z') -{ 3 }-> 2 :|: z = 2, z' = 3, 2 = 2
   a__U42(z, z') -{ 3 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2
   a__U42(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 3, X >= 0, 2 = X
   a__U42(z, z') -{ 3 }-> 1 + X :|: z = 2, z' >= 0, X >= 0, 1 + z' = X
   a__U42(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__U43(z) -{ 1 }-> 2 :|: z = 2
   a__U43(z) -{ 1 }-> 1 + z :|: z >= 0
   a__U51(z, z', z'') -{ 2 }-> a__U52(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   a__U51(z, z', z'') -{ 2 }-> a__U52(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') :|: z = 2, z' - 1 >= 0, z'' >= 0
   a__U51(z, z', z'') -{ 2 }-> a__U52(2, z'') :|: z = 2, z'' >= 0, z' = 0
   a__U51(z, z', z'') -{ 2 }-> a__U52(1 + z', z'') :|: z = 2, z' >= 0, z'' >= 0
   a__U51(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0
   a__U52(z, z') -{ 2 }-> a__U53(a__U61(a__and(a__isNatKind(V111), 1 + V25), V111, V25)) :|: z = 2, V25 >= 0, z' = 1 + V111 + V25, V111 >= 0
   a__U52(z, z') -{ 2 }-> a__U53(a__U51(a__and(a__isNatKind(V110), 1 + V24), V110, V24)) :|: z = 2, V110 >= 0, V24 >= 0, z' = 1 + V110 + V24
   a__U52(z, z') -{ 3 }-> 2 :|: z = 2, z' = 1, 2 = 2
   a__U52(z, z') -{ 3 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2
   a__U52(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 1, X >= 0, 2 = X
   a__U52(z, z') -{ 3 }-> 1 + X :|: z = 2, z' >= 0, X >= 0, 1 + z' = X
   a__U52(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__U53(z) -{ 1 }-> 2 :|: z = 2
   a__U53(z) -{ 1 }-> 1 + z :|: z >= 0
   a__U61(z, z', z'') -{ 2 }-> a__U62(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   a__U61(z, z', z'') -{ 2 }-> a__U62(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   a__U61(z, z', z'') -{ 2 }-> a__U62(2, z'') :|: z = 2, z'' >= 0, z' = 0
   a__U61(z, z', z'') -{ 2 }-> a__U62(1 + z', z'') :|: z = 2, z' >= 0, z'' >= 0
   a__U61(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0
   a__U62(z, z') -{ 2 }-> a__U63(a__U41(a__and(a__isNatKind(V114), 1 + V26), V114, V26)) :|: z = 2, z' = 1 + V114 + V26, V114 >= 0, V26 >= 0
   a__U62(z, z') -{ 2 }-> a__U63(a__U31(a__isNatIListKind(z'), z')) :|: z = 2, z' >= 0
   a__U62(z, z') -{ 3 }-> 2 :|: z = 2, z' = 3, 2 = 2
   a__U62(z, z') -{ 3 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2
   a__U62(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 3, X >= 0, 2 = X
   a__U62(z, z') -{ 3 }-> 1 + X :|: z = 2, z' >= 0, X >= 0, 1 + z' = X
   a__U62(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__U63(z) -{ 1 }-> 2 :|: z = 2
   a__U63(z) -{ 1 }-> 1 + z :|: z >= 0
   a__U71(z, z') -{ 1 }-> 1 + a__length(mark(z')) :|: z = 2, z' >= 0
   a__U71(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__U81(z) -{ 1 }-> 1 :|: z = 2
   a__U81(z) -{ 1 }-> 1 + z :|: z >= 0
   a__U91(z, z', z'', z1) -{ 1 }-> 1 + mark(z1) + (1 + z'' + z') :|: z = 2, z'' >= 0, z' >= 0, z1 >= 0
   a__U91(z, z', z'', z1) -{ 1 }-> 1 + z + z' + z'' + z1 :|: z >= 0, z'' >= 0, z' >= 0, z1 >= 0
   a__and(z, z') -{ 1 }-> mark(z') :|: z = 2, z' >= 0
   a__and(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__isNat(z) -{ 2 }-> a__U21(a__isNatKind(z - 2), 1 + (z - 2)) :|: z - 2 >= 0
   a__isNat(z) -{ 2 }-> a__U21(a__isNatIListKind(z - 2), 1 + (z - 2)) :|: z - 2 >= 0
   a__isNat(z) -{ 2 }-> a__U21(2, 0) :|: z = 1 + 0
   a__isNat(z) -{ 2 }-> a__U21(1 + (z - 1), z - 1) :|: z - 1 >= 0
   a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V115), 1 + V27), 1 + V115 + V27) :|: z = 1 + (1 + V115 + V27), V115 >= 0, V27 >= 0
   a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V116), 1 + V28), 1 + V116 + V28) :|: V28 >= 0, z = 1 + (1 + V116 + V28), V116 >= 0
   a__isNat(z) -{ 2 }-> a__U11(2, 3) :|: z = 1 + 3
   a__isNat(z) -{ 2 }-> a__U11(2, 1) :|: z = 1 + 1
   a__isNat(z) -{ 2 }-> a__U11(1 + (z - 1), z - 1) :|: z - 1 >= 0
   a__isNat(z) -{ 1 }-> 2 :|: z = 0
   a__isNat(z) -{ 1 }-> 1 + z :|: z >= 0
   a__isNatIList(z) -{ 2 }-> a__U41(a__and(a__isNatKind(V122), 1 + V2), 1 + V122, V2) :|: z = 1 + (1 + V122) + V2, V2 >= 0, V122 >= 0
   a__isNatIList(z) -{ 2 }-> a__U41(a__and(a__isNatIListKind(V121), 1 + V2), 1 + V121, V2) :|: V121 >= 0, z = 1 + (1 + V121) + V2, V2 >= 0
   a__isNatIList(z) -{ 2 }-> a__U41(a__and(2, 1 + (z - 1)), 0, z - 1) :|: z - 1 >= 0
   a__isNatIList(z) -{ 2 }-> a__U41(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatIList(z) -{ 2 }-> a__U31(a__and(a__isNatKind(V119), 1 + V29), 1 + V119 + V29) :|: V29 >= 0, z = 1 + V119 + V29, V119 >= 0
   a__isNatIList(z) -{ 2 }-> a__U31(a__and(a__isNatKind(V120), 1 + V210), 1 + V120 + V210) :|: V120 >= 0, z = 1 + V120 + V210, V210 >= 0
   a__isNatIList(z) -{ 2 }-> a__U31(2, 3) :|: z = 3
   a__isNatIList(z) -{ 2 }-> a__U31(2, 1) :|: z = 1
   a__isNatIList(z) -{ 2 }-> a__U31(1 + z, z) :|: z >= 0
   a__isNatIList(z) -{ 1 }-> 2 :|: z = 3
   a__isNatIList(z) -{ 1 }-> 1 + z :|: z >= 0
   a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatKind(V124), 1 + V2) :|: V124 >= 0, V2 >= 0, z = 1 + (1 + V124) + V2
   a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatKind(V126), 1 + V2) :|: V2 >= 0, V126 >= 0, z = 1 + (1 + V126) + V2
   a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatIListKind(V123), 1 + V2) :|: V2 >= 0, z = 1 + (1 + V123) + V2, V123 >= 0
   a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatIListKind(V125), 1 + V2) :|: V125 >= 0, z = 1 + (1 + V125) + V2, V2 >= 0
   a__isNatIListKind(z) -{ 2 }-> a__and(2, 1 + (z - 1)) :|: z - 1 >= 0
   a__isNatIListKind(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 1
   a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 3
   a__isNatIListKind(z) -{ 1 }-> 1 + z :|: z >= 0
   a__isNatKind(z) -{ 1 }-> a__isNatKind(z - 1) :|: z - 1 >= 0
   a__isNatKind(z) -{ 1 }-> a__isNatIListKind(z - 1) :|: z - 1 >= 0
   a__isNatKind(z) -{ 1 }-> 2 :|: z = 0
   a__isNatKind(z) -{ 1 }-> 1 + z :|: z >= 0
   a__isNatList(z) -{ 2 }-> a__U61(a__and(a__isNatKind(V130), 1 + V2), 1 + V130, V2) :|: z = 1 + (1 + V130) + V2, V130 >= 0, V2 >= 0
   a__isNatList(z) -{ 2 }-> a__U61(a__and(a__isNatIListKind(V129), 1 + V2), 1 + V129, V2) :|: z = 1 + (1 + V129) + V2, V2 >= 0, V129 >= 0
   a__isNatList(z) -{ 2 }-> a__U61(a__and(2, 1 + (z - 1)), 0, z - 1) :|: z - 1 >= 0
   a__isNatList(z) -{ 2 }-> a__U61(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatList(z) -{ 2 }-> a__U51(a__and(a__isNatKind(V128), 1 + V2), 1 + V128, V2) :|: V128 >= 0, V2 >= 0, z = 1 + (1 + V128) + V2
   a__isNatList(z) -{ 2 }-> a__U51(a__and(a__isNatIListKind(V127), 1 + V2), 1 + V127, V2) :|: V127 >= 0, V2 >= 0, z = 1 + (1 + V127) + V2
   a__isNatList(z) -{ 2 }-> a__U51(a__and(2, 1 + (z - 1)), 0, z - 1) :|: z - 1 >= 0
   a__isNatList(z) -{ 2 }-> a__U51(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatList(z) -{ 1 }-> 2 :|: z = 1
   a__isNatList(z) -{ 1 }-> 1 + z :|: z >= 0
   a__length(z) -{ 2 }-> a__U71(a__and(a__and(a__U61(a__and(a__isNatKind(V132), 1 + V212), V132, V212), 1 + (1 + V132 + V212)), 1 + (1 + N) + (1 + N)), 1 + V132 + V212) :|: z = 1 + N + (1 + V132 + V212), V132 >= 0, N >= 0, V212 >= 0
   a__length(z) -{ 2 }-> a__U71(a__and(a__and(a__U51(a__and(a__isNatKind(V131), 1 + V211), V131, V211), 1 + (1 + V131 + V211)), 1 + (1 + N) + (1 + N)), 1 + V131 + V211) :|: V131 >= 0, z = 1 + N + (1 + V131 + V211), V211 >= 0, N >= 0
   a__length(z) -{ 2 }-> a__U71(a__and(a__and(2, 1 + 1), 1 + (1 + (z - 2)) + (1 + (z - 2))), 1) :|: z - 2 >= 0
   a__length(z) -{ 2 }-> a__U71(a__and(a__and(1 + L, 1 + L), 1 + (1 + N) + (1 + N)), L) :|: z = 1 + N + L, L >= 0, N >= 0
   a__length(z) -{ 1 }-> 0 :|: z = 1
   a__length(z) -{ 1 }-> 1 + z :|: z >= 0
   a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(a__U41(a__and(a__isNatKind(V134), 1 + V214), V134, V214), 1 + (1 + V134 + V214)), 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) + (1 + (1 + N) + (1 + N))), 1 + V134 + V214, z - 1, N) :|: V214 >= 0, z' = 1 + N + (1 + V134 + V214), z - 1 >= 0, V134 >= 0, N >= 0
   a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(a__U31(a__isNatIListKind(IL), IL), 1 + IL), 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) + (1 + (1 + N) + (1 + N))), IL, z - 1, N) :|: z - 1 >= 0, IL >= 0, z' = 1 + N + IL, N >= 0
   a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(2, 1 + 3), 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) + (1 + (1 + (z' - 4)) + (1 + (z' - 4)))), 3, z - 1, z' - 4) :|: z - 1 >= 0, z' - 4 >= 0
   a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(1 + IL, 1 + IL), 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) + (1 + (1 + N) + (1 + N))), IL, z - 1, N) :|: z - 1 >= 0, IL >= 0, z' = 1 + N + IL, N >= 0
   a__take(z, z') -{ 2 }-> a__U81(a__and(a__U41(a__and(a__isNatKind(V133), 1 + V213), V133, V213), 1 + (1 + V133 + V213))) :|: V213 >= 0, z' = 1 + V133 + V213, z = 0, V133 >= 0
   a__take(z, z') -{ 2 }-> a__U81(a__and(a__U31(a__isNatIListKind(z'), z'), 1 + z')) :|: z = 0, z' >= 0
   a__take(z, z') -{ 2 }-> a__U81(a__and(2, 1 + 3)) :|: z' = 3, z = 0
   a__take(z, z') -{ 2 }-> a__U81(a__and(1 + z', 1 + z')) :|: z = 0, z' >= 0
   a__take(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__zeros -{ 1 }-> 3 :|: 
   a__zeros -{ 1 }-> 1 + 0 + 3 :|: 
   mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__length(mark(z - 1)) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__isNatList(z - 1) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__isNatKind(z - 1) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__isNatIListKind(z - 1) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__isNatIList(z - 1) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__isNat(z - 1) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__and(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U91(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 1 }-> a__U81(mark(z - 1)) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__U71(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U63(mark(z - 1)) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__U62(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U61(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U53(mark(z - 1)) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__U52(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U51(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U43(mark(z - 1)) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__U42(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U41(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U32(mark(z - 1)) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U22(mark(z - 1)) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__U21(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U12(mark(z - 1)) :|: z - 1 >= 0
   mark(z) -{ 1 }-> a__U11(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 2 }-> 3 :|: z = 3
   mark(z) -{ 1 }-> 2 :|: z = 2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0
   mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 2 }-> 1 + 0 + 3 :|: z = 3


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

(19) CompletionProof (UPPER BOUND(ID))
The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:
none

And the following fresh constants: none

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

(20)
Obligation:
Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is:

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

   a__zeros -> cons(0, zeros) [1]
   a__U11(tt, V1) -> a__U12(a__isNatList(V1)) [1]
   a__U12(tt) -> tt [1]
   a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1]
   a__U22(tt) -> tt [1]
   a__U31(tt, V) -> a__U32(a__isNatList(V)) [1]
   a__U32(tt) -> tt [1]
   a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2) [1]
   a__U42(tt, V2) -> a__U43(a__isNatIList(V2)) [1]
   a__U43(tt) -> tt [1]
   a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2) [1]
   a__U52(tt, V2) -> a__U53(a__isNatList(V2)) [1]
   a__U53(tt) -> tt [1]
   a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2) [1]
   a__U62(tt, V2) -> a__U63(a__isNatIList(V2)) [1]
   a__U63(tt) -> tt [1]
   a__U71(tt, L) -> s(a__length(mark(L))) [1]
   a__U81(tt) -> nil [1]
   a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1]
   a__and(tt, X) -> mark(X) [1]
   a__isNat(0) -> tt [1]
   a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) [1]
   a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1]
   a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) [1]
   a__isNatIList(zeros) -> tt [1]
   a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1]
   a__isNatIListKind(nil) -> tt [1]
   a__isNatIListKind(zeros) -> tt [1]
   a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1]
   a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1]
   a__isNatKind(0) -> tt [1]
   a__isNatKind(length(V1)) -> a__isNatIListKind(V1) [1]
   a__isNatKind(s(V1)) -> a__isNatKind(V1) [1]
   a__isNatList(nil) -> tt [1]
   a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1]
   a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1]
   a__length(nil) -> 0 [1]
   a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) [1]
   a__take(0, IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) [1]
   a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) [1]
   mark(zeros) -> a__zeros [1]
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1]
   mark(U12(X)) -> a__U12(mark(X)) [1]
   mark(isNatList(X)) -> a__isNatList(X) [1]
   mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1]
   mark(U22(X)) -> a__U22(mark(X)) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1]
   mark(U32(X)) -> a__U32(mark(X)) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(U42(X1, X2)) -> a__U42(mark(X1), X2) [1]
   mark(U43(X)) -> a__U43(mark(X)) [1]
   mark(isNatIList(X)) -> a__isNatIList(X) [1]
   mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) [1]
   mark(U52(X1, X2)) -> a__U52(mark(X1), X2) [1]
   mark(U53(X)) -> a__U53(mark(X)) [1]
   mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) [1]
   mark(U62(X1, X2)) -> a__U62(mark(X1), X2) [1]
   mark(U63(X)) -> a__U63(mark(X)) [1]
   mark(U71(X1, X2)) -> a__U71(mark(X1), X2) [1]
   mark(length(X)) -> a__length(mark(X)) [1]
   mark(U81(X)) -> a__U81(mark(X)) [1]
   mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) [1]
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1]
   mark(and(X1, X2)) -> a__and(mark(X1), X2) [1]
   mark(isNatIListKind(X)) -> a__isNatIListKind(X) [1]
   mark(isNatKind(X)) -> a__isNatKind(X) [1]
   mark(cons(X1, X2)) -> cons(mark(X1), X2) [1]
   mark(0) -> 0 [1]
   mark(tt) -> tt [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(nil) -> nil [1]
   a__zeros -> zeros [1]
   a__U11(X1, X2) -> U11(X1, X2) [1]
   a__U12(X) -> U12(X) [1]
   a__isNatList(X) -> isNatList(X) [1]
   a__U21(X1, X2) -> U21(X1, X2) [1]
   a__U22(X) -> U22(X) [1]
   a__isNat(X) -> isNat(X) [1]
   a__U31(X1, X2) -> U31(X1, X2) [1]
   a__U32(X) -> U32(X) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__U42(X1, X2) -> U42(X1, X2) [1]
   a__U43(X) -> U43(X) [1]
   a__isNatIList(X) -> isNatIList(X) [1]
   a__U51(X1, X2, X3) -> U51(X1, X2, X3) [1]
   a__U52(X1, X2) -> U52(X1, X2) [1]
   a__U53(X) -> U53(X) [1]
   a__U61(X1, X2, X3) -> U61(X1, X2, X3) [1]
   a__U62(X1, X2) -> U62(X1, X2) [1]
   a__U63(X) -> U63(X) [1]
   a__U71(X1, X2) -> U71(X1, X2) [1]
   a__length(X) -> length(X) [1]
   a__U81(X) -> U81(X) [1]
   a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) [1]
   a__take(X1, X2) -> take(X1, X2) [1]
   a__and(X1, X2) -> and(X1, X2) [1]
   a__isNatIListKind(X) -> isNatIListKind(X) [1]
   a__isNatKind(X) -> isNatKind(X) [1]

The TRS has the following type information:
a__zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
cons :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
0 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
tt :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
s :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
mark :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
nil :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
a__take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91
U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91

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

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

   0 => 0
   zeros => 3
   tt => 2
   nil => 1

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

(22)
Obligation:
Complexity RNTS consisting of the following rules:

   a__U11(z, z') -{ 1 }-> a__U12(a__isNatList(V1)) :|: z = 2, V1 >= 0, z' = V1
   a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U12(z) -{ 1 }-> 2 :|: z = 2
   a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U21(z, z') -{ 1 }-> a__U22(a__isNat(V1)) :|: z = 2, V1 >= 0, z' = V1
   a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U22(z) -{ 1 }-> 2 :|: z = 2
   a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U31(z, z') -{ 1 }-> a__U32(a__isNatList(V)) :|: z = 2, z' = V, V >= 0
   a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U32(z) -{ 1 }-> 2 :|: z = 2
   a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U41(z, z', z'') -{ 1 }-> a__U42(a__isNat(V1), V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1
   a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U42(z, z') -{ 1 }-> a__U43(a__isNatIList(V2)) :|: z = 2, z' = V2, V2 >= 0
   a__U42(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U43(z) -{ 1 }-> 2 :|: z = 2
   a__U43(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U51(z, z', z'') -{ 1 }-> a__U52(a__isNat(V1), V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1
   a__U51(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U52(z, z') -{ 1 }-> a__U53(a__isNatList(V2)) :|: z = 2, z' = V2, V2 >= 0
   a__U52(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U53(z) -{ 1 }-> 2 :|: z = 2
   a__U53(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U61(z, z', z'') -{ 1 }-> a__U62(a__isNat(V1), V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1
   a__U61(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U62(z, z') -{ 1 }-> a__U63(a__isNatIList(V2)) :|: z = 2, z' = V2, V2 >= 0
   a__U62(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U63(z) -{ 1 }-> 2 :|: z = 2
   a__U63(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U71(z, z') -{ 1 }-> 1 + a__length(mark(L)) :|: z = 2, L >= 0, z' = L
   a__U71(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U81(z) -{ 1 }-> 1 :|: z = 2
   a__U81(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U91(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0
   a__U91(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3
   a__and(z, z') -{ 1 }-> mark(X) :|: z = 2, z' = X, X >= 0
   a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__isNat(z) -{ 1 }-> a__U21(a__isNatKind(V1), V1) :|: z = 1 + V1, V1 >= 0
   a__isNat(z) -{ 1 }-> a__U11(a__isNatIListKind(V1), V1) :|: z = 1 + V1, V1 >= 0
   a__isNat(z) -{ 1 }-> 2 :|: z = 0
   a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatIList(z) -{ 1 }-> a__U41(a__and(a__isNatKind(V1), 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatIList(z) -{ 1 }-> a__U31(a__isNatIListKind(V), V) :|: z = V, V >= 0
   a__isNatIList(z) -{ 1 }-> 2 :|: z = 3
   a__isNatIList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatIListKind(z) -{ 1 }-> a__and(a__isNatKind(V1), 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 1
   a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 3
   a__isNatIListKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatKind(z) -{ 1 }-> a__isNatKind(V1) :|: z = 1 + V1, V1 >= 0
   a__isNatKind(z) -{ 1 }-> a__isNatIListKind(V1) :|: z = 1 + V1, V1 >= 0
   a__isNatKind(z) -{ 1 }-> 2 :|: z = 0
   a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNatList(z) -{ 1 }-> a__U61(a__and(a__isNatKind(V1), 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatList(z) -{ 1 }-> a__U51(a__and(a__isNatKind(V1), 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNatList(z) -{ 1 }-> 2 :|: z = 1
   a__isNatList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__length(z) -{ 1 }-> a__U71(a__and(a__and(a__isNatList(L), 1 + L), 1 + (1 + N) + (1 + N)), L) :|: z = 1 + N + L, L >= 0, N >= 0
   a__length(z) -{ 1 }-> 0 :|: z = 1
   a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__take(z, z') -{ 1 }-> a__U91(a__and(a__and(a__isNatIList(IL), 1 + IL), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0
   a__take(z, z') -{ 1 }-> a__U81(a__and(a__isNatIList(IL), 1 + IL)) :|: z' = IL, z = 0, IL >= 0
   a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__zeros -{ 1 }-> 3 :|: 
   a__zeros -{ 1 }-> 1 + 0 + 3 :|: 
   mark(z) -{ 1 }-> a__zeros :|: z = 3
   mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__length(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatList(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatIListKind(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNatIList(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__and(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U91(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0
   mark(z) -{ 1 }-> a__U81(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U71(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U63(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U62(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U61(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U53(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U52(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U51(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U43(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U42(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U41(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U32(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U22(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U21(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U12(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U11(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> 2 :|: z = 2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2

Only complete derivations are relevant for the runtime complexity.

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

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

(24)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__ZEROS -> c
   A__ZEROS -> c1
   A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U11(z0, z1) -> c3
   A__U12(tt) -> c4
   A__U12(z0) -> c5
   A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0))
   A__U21(z0, z1) -> c7
   A__U22(tt) -> c8
   A__U22(z0) -> c9
   A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U31(z0, z1) -> c11
   A__U32(tt) -> c12
   A__U32(z0) -> c13
   A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0))
   A__U41(z0, z1, z2) -> c15
   A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__U42(z0, z1) -> c17
   A__U43(tt) -> c18
   A__U43(z0) -> c19
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
   A__U51(z0, z1, z2) -> c21
   A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U52(z0, z1) -> c23
   A__U53(tt) -> c24
   A__U53(z0) -> c25
   A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0))
   A__U61(z0, z1, z2) -> c27
   A__U62(tt, z0) -> c28(A__U63(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__U62(z0, z1) -> c29
   A__U63(tt) -> c30
   A__U63(z0) -> c31
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U71(z0, z1) -> c33
   A__U81(tt) -> c34
   A__U81(z0) -> c35
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__U91(z0, z1, z2, z3) -> c37
   A__AND(tt, z0) -> c38(MARK(z0))
   A__AND(z0, z1) -> c39
   A__ISNAT(0) -> c40
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNAT(z0) -> c43
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(zeros) -> c45
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c47
   A__ISNATILISTKIND(nil) -> c48
   A__ISNATILISTKIND(zeros) -> c49
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(z0) -> c52
   A__ISNATKIND(0) -> c53
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATKIND(z0) -> c56
   A__ISNATLIST(nil) -> c57
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(z0) -> c60
   A__LENGTH(nil) -> c61
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__LENGTH(z0) -> c63
   A__TAKE(0, z0) -> c64(A__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   A__TAKE(z0, z1) -> c66
   MARK(zeros) -> c67(A__ZEROS)
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(U12(z0)) -> c69(A__U12(mark(z0)), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(U22(z0)) -> c72(A__U22(mark(z0)), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U32(z0)) -> c75(A__U32(mark(z0)), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(U43(z0)) -> c78(A__U43(mark(z0)), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U53(z0)) -> c82(A__U53(mark(z0)), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U63(z0)) -> c85(A__U63(mark(z0)), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U81(z0)) -> c88(A__U81(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(0) -> c96
   MARK(tt) -> c97
   MARK(s(z0)) -> c98(MARK(z0))
   MARK(nil) -> c99
S tuples:
   A__ZEROS -> c
   A__ZEROS -> c1
   A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U11(z0, z1) -> c3
   A__U12(tt) -> c4
   A__U12(z0) -> c5
   A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0))
   A__U21(z0, z1) -> c7
   A__U22(tt) -> c8
   A__U22(z0) -> c9
   A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U31(z0, z1) -> c11
   A__U32(tt) -> c12
   A__U32(z0) -> c13
   A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0))
   A__U41(z0, z1, z2) -> c15
   A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__U42(z0, z1) -> c17
   A__U43(tt) -> c18
   A__U43(z0) -> c19
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
   A__U51(z0, z1, z2) -> c21
   A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U52(z0, z1) -> c23
   A__U53(tt) -> c24
   A__U53(z0) -> c25
   A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0))
   A__U61(z0, z1, z2) -> c27
   A__U62(tt, z0) -> c28(A__U63(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__U62(z0, z1) -> c29
   A__U63(tt) -> c30
   A__U63(z0) -> c31
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U71(z0, z1) -> c33
   A__U81(tt) -> c34
   A__U81(z0) -> c35
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__U91(z0, z1, z2, z3) -> c37
   A__AND(tt, z0) -> c38(MARK(z0))
   A__AND(z0, z1) -> c39
   A__ISNAT(0) -> c40
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNAT(z0) -> c43
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(zeros) -> c45
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c47
   A__ISNATILISTKIND(nil) -> c48
   A__ISNATILISTKIND(zeros) -> c49
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(z0) -> c52
   A__ISNATKIND(0) -> c53
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATKIND(z0) -> c56
   A__ISNATLIST(nil) -> c57
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(z0) -> c60
   A__LENGTH(nil) -> c61
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__LENGTH(z0) -> c63
   A__TAKE(0, z0) -> c64(A__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   A__TAKE(z0, z1) -> c66
   MARK(zeros) -> c67(A__ZEROS)
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(U12(z0)) -> c69(A__U12(mark(z0)), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(U22(z0)) -> c72(A__U22(mark(z0)), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U32(z0)) -> c75(A__U32(mark(z0)), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(U43(z0)) -> c78(A__U43(mark(z0)), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U53(z0)) -> c82(A__U53(mark(z0)), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U63(z0)) -> c85(A__U63(mark(z0)), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U81(z0)) -> c88(A__U81(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(0) -> c96
   MARK(tt) -> c97
   MARK(s(z0)) -> c98(MARK(z0))
   MARK(nil) -> c99
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__ZEROS, A__U11_2, A__U12_1, A__U21_2, A__U22_1, A__U31_2, A__U32_1, A__U41_3, A__U42_2, A__U43_1, A__U51_3, A__U52_2, A__U53_1, A__U61_3, A__U62_2, A__U63_1, A__U71_2, A__U81_1, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1

Compound Symbols:   c, c1, c2_2, c3, c4, c5, c6_2, c7, c8, c9, c10_2, c11, c12, c13, c14_2, c15, c16_2, c17, c18, c19, c20_2, c21, c22_2, c23, c24, c25, c26_2, c27, c28_2, c29, c30, c31, c32_2, c33, c34, c35, c36_1, c37, c38_1, c39, c40, c41_2, c42_2, c43, c44_2, c45, c46_3, c47, c48, c49, c50_2, c51_2, c52, c53, c54_1, c55_1, c56, c57, c58_3, c59_3, c60, c61, c62_4, c63, c64_3, c65_4, c66, c67_1, c68_2, c69_2, c70_1, c71_2, c72_2, c73_1, c74_2, c75_2, c76_2, c77_2, c78_2, c79_1, c80_2, c81_2, c82_2, c83_2, c84_2, c85_2, c86_2, c87_2, c88_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c96, c97, c98_1, c99


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

(25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 46 trailing nodes:
   MARK(tt) -> c97
   MARK(0) -> c96
   A__U81(tt) -> c34
   A__TAKE(z0, z1) -> c66
   A__ISNATLIST(nil) -> c57
   A__ISNATILISTKIND(zeros) -> c49
   A__U11(z0, z1) -> c3
   A__LENGTH(z0) -> c63
   A__U53(tt) -> c24
   A__U53(z0) -> c25
   A__ZEROS -> c
   A__ISNATILISTKIND(z0) -> c52
   A__U81(z0) -> c35
   A__U51(z0, z1, z2) -> c21
   A__U12(tt) -> c4
   A__ISNATLIST(z0) -> c60
   A__U91(z0, z1, z2, z3) -> c37
   A__U12(z0) -> c5
   A__ISNATILISTKIND(nil) -> c48
   A__U32(tt) -> c12
   A__ISNATKIND(0) -> c53
   A__U71(z0, z1) -> c33
   A__ISNAT(z0) -> c43
   A__ISNATILIST(z0) -> c47
   A__U61(z0, z1, z2) -> c27
   A__U22(tt) -> c8
   A__U41(z0, z1, z2) -> c15
   A__U31(z0, z1) -> c11
   A__ISNAT(0) -> c40
   MARK(zeros) -> c67(A__ZEROS)
   A__U42(z0, z1) -> c17
   A__U43(z0) -> c19
   A__AND(z0, z1) -> c39
   A__U21(z0, z1) -> c7
   A__ZEROS -> c1
   A__U63(tt) -> c30
   A__U52(z0, z1) -> c23
   A__LENGTH(nil) -> c61
   A__U63(z0) -> c31
   A__ISNATKIND(z0) -> c56
   A__ISNATILIST(zeros) -> c45
   A__U62(z0, z1) -> c29
   A__U43(tt) -> c18
   A__U32(z0) -> c13
   A__U22(z0) -> c9
   MARK(nil) -> c99

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

(26)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0))
   A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
   A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0))
   A__U62(tt, z0) -> c28(A__U63(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(0, z0) -> c64(A__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(U12(z0)) -> c69(A__U12(mark(z0)), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(U22(z0)) -> c72(A__U22(mark(z0)), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U32(z0)) -> c75(A__U32(mark(z0)), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(U43(z0)) -> c78(A__U43(mark(z0)), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U53(z0)) -> c82(A__U53(mark(z0)), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U63(z0)) -> c85(A__U63(mark(z0)), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U81(z0)) -> c88(A__U81(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
S tuples:
   A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0))
   A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
   A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0))
   A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0))
   A__U62(tt, z0) -> c28(A__U63(a__isNatIList(z0)), A__ISNATILIST(z0))
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(0, z0) -> c64(A__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(U12(z0)) -> c69(A__U12(mark(z0)), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(U22(z0)) -> c72(A__U22(mark(z0)), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U32(z0)) -> c75(A__U32(mark(z0)), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(U43(z0)) -> c78(A__U43(mark(z0)), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U53(z0)) -> c82(A__U53(mark(z0)), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U63(z0)) -> c85(A__U63(mark(z0)), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U81(z0)) -> c88(A__U81(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U21_2, A__U31_2, A__U41_3, A__U42_2, A__U51_3, A__U52_2, A__U61_3, A__U62_2, A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1

Compound Symbols:   c2_2, c6_2, c10_2, c14_2, c16_2, c20_2, c22_2, c26_2, c28_2, c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c64_3, c65_4, c68_2, c69_2, c70_1, c71_2, c72_2, c73_1, c74_2, c75_2, c76_2, c77_2, c78_2, c79_1, c80_2, c81_2, c82_2, c83_2, c84_2, c85_2, c86_2, c87_2, c88_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1


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

(27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 14 trailing tuple parts
----------------------------------------

(28)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0))
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
   A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0))
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
S tuples:
   A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0))
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
   A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0))
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2

Compound Symbols:   c14_2, c20_2, c26_2, c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1


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

(29) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) by 
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1), A__ISNAT(0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, z0, x1) -> c14(A__U42(isNat(z0), x1), A__ISNAT(z0))

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

(30)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
   A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0))
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1), A__ISNAT(0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, z0, x1) -> c14(A__U42(isNat(z0), x1), A__ISNAT(z0))
S tuples:
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
   A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0))
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1), A__ISNAT(0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, z0, x1) -> c14(A__U42(isNat(z0), x1), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U51_3, A__U61_3, A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3

Compound Symbols:   c20_2, c26_2, c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2


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

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

(32)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
   A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0))
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
S tuples:
   A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0))
   A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0))
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U51_3, A__U61_3, A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3

Compound Symbols:   c20_2, c26_2, c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1


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

(33) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) by 
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1), A__ISNAT(0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, z0, x1) -> c20(A__U52(isNat(z0), x1), A__ISNAT(z0))

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

(34)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0))
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1), A__ISNAT(0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, z0, x1) -> c20(A__U52(isNat(z0), x1), A__ISNAT(z0))
S tuples:
   A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0))
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1), A__ISNAT(0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, z0, x1) -> c20(A__U52(isNat(z0), x1), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U61_3, A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3

Compound Symbols:   c26_2, c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2


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

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0))
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
S tuples:
   A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0))
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U61_3, A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3

Compound Symbols:   c26_2, c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1


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

(37) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) by 
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1), A__ISNAT(0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, z0, x1) -> c26(A__U62(isNat(z0), x1), A__ISNAT(z0))

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1), A__ISNAT(0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, z0, x1) -> c26(A__U62(isNat(z0), x1), A__ISNAT(z0))
S tuples:
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1), A__ISNAT(0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, z0, x1) -> c26(A__U62(isNat(z0), x1), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3

Compound Symbols:   c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2


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

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
S tuples:
   A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0))
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3

Compound Symbols:   c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1


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

(41) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) by 
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros), MARK(zeros))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, 0) -> c32(A__LENGTH(0), MARK(0))
   A__U71(tt, tt) -> c32(A__LENGTH(tt), MARK(tt))
   A__U71(tt, s(z0)) -> c32(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   A__U71(tt, nil) -> c32(A__LENGTH(nil), MARK(nil))

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros), MARK(zeros))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, 0) -> c32(A__LENGTH(0), MARK(0))
   A__U71(tt, tt) -> c32(A__LENGTH(tt), MARK(tt))
   A__U71(tt, s(z0)) -> c32(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   A__U71(tt, nil) -> c32(A__LENGTH(nil), MARK(nil))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros), MARK(zeros))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, 0) -> c32(A__LENGTH(0), MARK(0))
   A__U71(tt, tt) -> c32(A__LENGTH(tt), MARK(tt))
   A__U71(tt, s(z0)) -> c32(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   A__U71(tt, nil) -> c32(A__LENGTH(nil), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2

Compound Symbols:   c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2


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

(43) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   A__U71(tt, 0) -> c32(A__LENGTH(0), MARK(0))
   A__U71(tt, nil) -> c32(A__LENGTH(nil), MARK(nil))
   A__U71(tt, tt) -> c32(A__LENGTH(tt), MARK(tt))

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros), MARK(zeros))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, s(z0)) -> c32(A__LENGTH(s(mark(z0))), MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros), MARK(zeros))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, s(z0)) -> c32(A__LENGTH(s(mark(z0))), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2

Compound Symbols:   c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2


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

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2

Compound Symbols:   c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1


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

(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) by 
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil), A__ISNATILISTKIND(nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros), A__ISNATILISTKIND(zeros))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(z0)) -> c41(A__U11(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))

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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil), A__ISNATILISTKIND(nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros), A__ISNATILISTKIND(zeros))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(z0)) -> c41(A__U11(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil), A__ISNATILISTKIND(nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros), A__ISNATILISTKIND(zeros))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(z0)) -> c41(A__U11(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2

Compound Symbols:   c36_1, c38_1, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2


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

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2

Compound Symbols:   c36_1, c38_1, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) by 
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0), A__ISNATKIND(0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(z0)) -> c42(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0))

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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0), A__ISNATKIND(0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(z0)) -> c42(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0), A__ISNATKIND(0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(z0)) -> c42(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1

Compound Symbols:   c36_1, c38_1, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2


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

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1

Compound Symbols:   c36_1, c38_1, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) by 
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil), A__ISNATILISTKIND(nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros), A__ISNATILISTKIND(zeros))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(z0) -> c44(A__U31(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))

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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil), A__ISNATILISTKIND(nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros), A__ISNATILISTKIND(zeros))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(z0) -> c44(A__U31(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil), A__ISNATILISTKIND(nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros), A__ISNATILISTKIND(zeros))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(z0) -> c44(A__U31(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1

Compound Symbols:   c36_1, c38_1, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2


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

(57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1

Compound Symbols:   c36_1, c38_1, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) by 
   A__ISNATILIST(cons(x0, x1)) -> c46(A__U41(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))

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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__U41(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__U41(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1

Compound Symbols:   c36_1, c38_1, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3


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

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1

Compound Symbols:   c36_1, c38_1, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) by 
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)), A__ISNATKIND(0))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__AND(isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)), A__ISNATKIND(0))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__AND(isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)), A__ISNATKIND(0))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__AND(isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1

Compound Symbols:   c36_1, c38_1, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2


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

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1

Compound Symbols:   c36_1, c38_1, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1


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

(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) by 
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)), A__ISNATKIND(0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__AND(isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)), A__ISNATKIND(0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__AND(isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)), A__ISNATKIND(0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__AND(isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2


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

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) by 
   A__ISNATLIST(cons(x0, x1)) -> c58(A__U51(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__U51(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__U51(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3


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

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) by 
   A__ISNATLIST(take(x0, x1)) -> c59(A__U61(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(x0, x1)) -> c59(A__U61(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(x0, x1)) -> c59(A__U61(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3


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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) by 
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(and(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__U71(a__and(a__and(tt, isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), nil), A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)), A__ISNATLIST(nil))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(and(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__U71(a__and(a__and(tt, isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), nil), A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)), A__ISNATLIST(nil))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(and(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__U71(a__and(a__and(tt, isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), nil), A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)), A__ISNATLIST(nil))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4


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

(81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) by 
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(and(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(and(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(and(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4


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

(85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) by 
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1), MARK(zeros))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(cons(z0, z1), x1)) -> c68(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U11(0, x1)) -> c68(A__U11(0, x1), MARK(0))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1), MARK(tt))
   MARK(U11(s(z0), x1)) -> c68(A__U11(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U11(nil, x1)) -> c68(A__U11(nil, x1), MARK(nil))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1), MARK(zeros))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(cons(z0, z1), x1)) -> c68(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U11(0, x1)) -> c68(A__U11(0, x1), MARK(0))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1), MARK(tt))
   MARK(U11(s(z0), x1)) -> c68(A__U11(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U11(nil, x1)) -> c68(A__U11(nil, x1), MARK(nil))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1), MARK(zeros))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(cons(z0, z1), x1)) -> c68(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U11(0, x1)) -> c68(A__U11(0, x1), MARK(0))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1), MARK(tt))
   MARK(U11(s(z0), x1)) -> c68(A__U11(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U11(nil, x1)) -> c68(A__U11(nil, x1), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2


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

(89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U11(0, x1)) -> c68(A__U11(0, x1), MARK(0))
   MARK(U11(nil, x1)) -> c68(A__U11(nil, x1), MARK(nil))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1), MARK(zeros))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(cons(z0, z1), x1)) -> c68(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1), MARK(tt))
   MARK(U11(s(z0), x1)) -> c68(A__U11(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1), MARK(zeros))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(cons(z0, z1), x1)) -> c68(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1), MARK(tt))
   MARK(U11(s(z0), x1)) -> c68(A__U11(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2


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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1


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

(93) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) by 
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1), MARK(zeros))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(cons(z0, z1), x1)) -> c71(A__U21(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U21(0, x1)) -> c71(A__U21(0, x1), MARK(0))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1), MARK(tt))
   MARK(U21(s(z0), x1)) -> c71(A__U21(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U21(nil, x1)) -> c71(A__U21(nil, x1), MARK(nil))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1), MARK(zeros))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(cons(z0, z1), x1)) -> c71(A__U21(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U21(0, x1)) -> c71(A__U21(0, x1), MARK(0))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1), MARK(tt))
   MARK(U21(s(z0), x1)) -> c71(A__U21(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U21(nil, x1)) -> c71(A__U21(nil, x1), MARK(nil))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1), MARK(zeros))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(cons(z0, z1), x1)) -> c71(A__U21(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U21(0, x1)) -> c71(A__U21(0, x1), MARK(0))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1), MARK(tt))
   MARK(U21(s(z0), x1)) -> c71(A__U21(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U21(nil, x1)) -> c71(A__U21(nil, x1), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2


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

(95) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U21(nil, x1)) -> c71(A__U21(nil, x1), MARK(nil))
   MARK(U21(0, x1)) -> c71(A__U21(0, x1), MARK(0))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1), MARK(zeros))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(cons(z0, z1), x1)) -> c71(A__U21(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1), MARK(tt))
   MARK(U21(s(z0), x1)) -> c71(A__U21(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1), MARK(zeros))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(cons(z0, z1), x1)) -> c71(A__U21(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1), MARK(tt))
   MARK(U21(s(z0), x1)) -> c71(A__U21(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2


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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
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   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1))
   MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c71(MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1))
   MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c71(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1


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

(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) by 
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1), MARK(zeros))
   MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(cons(z0, z1), x1)) -> c74(A__U31(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U31(0, x1)) -> c74(A__U31(0, x1), MARK(0))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1), MARK(tt))
   MARK(U31(s(z0), x1)) -> c74(A__U31(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U31(nil, x1)) -> c74(A__U31(nil, x1), MARK(nil))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1))
   MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c71(MARK(s(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1), MARK(zeros))
   MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(cons(z0, z1), x1)) -> c74(A__U31(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U31(0, x1)) -> c74(A__U31(0, x1), MARK(0))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1), MARK(tt))
   MARK(U31(s(z0), x1)) -> c74(A__U31(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U31(nil, x1)) -> c74(A__U31(nil, x1), MARK(nil))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1))
   MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c71(MARK(s(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1), MARK(zeros))
   MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(cons(z0, z1), x1)) -> c74(A__U31(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U31(0, x1)) -> c74(A__U31(0, x1), MARK(0))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1), MARK(tt))
   MARK(U31(s(z0), x1)) -> c74(A__U31(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U31(nil, x1)) -> c74(A__U31(nil, x1), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2


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

(101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U31(0, x1)) -> c74(A__U31(0, x1), MARK(0))
   MARK(U31(nil, x1)) -> c74(A__U31(nil, x1), MARK(nil))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1))
   MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c71(MARK(s(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1), MARK(zeros))
   MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(cons(z0, z1), x1)) -> c74(A__U31(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1), MARK(tt))
   MARK(U31(s(z0), x1)) -> c74(A__U31(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1))
   MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c71(MARK(s(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1), MARK(zeros))
   MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(cons(z0, z1), x1)) -> c74(A__U31(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1), MARK(tt))
   MARK(U31(s(z0), x1)) -> c74(A__U31(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2


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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
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   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1))
   MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1)))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c74(MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1))
   MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c71(MARK(s(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1))
   MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1)))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c74(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1


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

(105) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) by 
   MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2), MARK(zeros))
   MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(cons(z0, z1), x1, x2)) -> c76(A__U41(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1)))
   MARK(U41(0, x1, x2)) -> c76(A__U41(0, x1, x2), MARK(0))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c76(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U41(nil, x1, x2)) -> c76(A__U41(nil, x1, x2), MARK(nil))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
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   MARK(U41(s(z0), x1, x2)) -> c76(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U41(nil, x1, x2)) -> c76(A__U41(nil, x1, x2), MARK(nil))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1))
   MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c71(MARK(s(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1))
   MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1)))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c74(MARK(s(z0)))
   MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2), MARK(zeros))
   MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(cons(z0, z1), x1, x2)) -> c76(A__U41(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1)))
   MARK(U41(0, x1, x2)) -> c76(A__U41(0, x1, x2), MARK(0))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c76(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U41(nil, x1, x2)) -> c76(A__U41(nil, x1, x2), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2


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

(107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U41(0, x1, x2)) -> c76(A__U41(0, x1, x2), MARK(0))
   MARK(U41(nil, x1, x2)) -> c76(A__U41(nil, x1, x2), MARK(nil))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1))
   MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c71(MARK(s(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1))
   MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1)))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c74(MARK(s(z0)))
   MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2), MARK(zeros))
   MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(cons(z0, z1), x1, x2)) -> c76(A__U41(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c76(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
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   MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1))
   MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1)))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c74(MARK(s(z0)))
   MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2), MARK(zeros))
   MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(cons(z0, z1), x1, x2)) -> c76(A__U41(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c76(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2


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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
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   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1))
   MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c71(MARK(s(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1))
   MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1)))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c74(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2))
   MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
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   MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2))
   MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1


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

(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) by 
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1), MARK(zeros))
   MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(cons(z0, z1), x1)) -> c77(A__U42(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U42(0, x1)) -> c77(A__U42(0, x1), MARK(0))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1), MARK(tt))
   MARK(U42(s(z0), x1)) -> c77(A__U42(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U42(nil, x1)) -> c77(A__U42(nil, x1), MARK(nil))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
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   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1))
   MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1)))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c74(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2))
   MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1), MARK(zeros))
   MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(cons(z0, z1), x1)) -> c77(A__U42(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U42(0, x1)) -> c77(A__U42(0, x1), MARK(0))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1), MARK(tt))
   MARK(U42(s(z0), x1)) -> c77(A__U42(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U42(nil, x1)) -> c77(A__U42(nil, x1), MARK(nil))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
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   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c74(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2))
   MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1), MARK(zeros))
   MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(cons(z0, z1), x1)) -> c77(A__U42(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U42(0, x1)) -> c77(A__U42(0, x1), MARK(0))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1), MARK(tt))
   MARK(U42(s(z0), x1)) -> c77(A__U42(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U42(nil, x1)) -> c77(A__U42(nil, x1), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2


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

(113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U42(nil, x1)) -> c77(A__U42(nil, x1), MARK(nil))
   MARK(U42(0, x1)) -> c77(A__U42(0, x1), MARK(0))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
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   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
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   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
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   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
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   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
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   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
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   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
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   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
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   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
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   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
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   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
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   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
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   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
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   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
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   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
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   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
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   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
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   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
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   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
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   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
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   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
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   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
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   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
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   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1))
   MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c71(MARK(s(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1))
   MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1)))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c74(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2))
   MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1), MARK(zeros))
   MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(cons(z0, z1), x1)) -> c77(A__U42(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1), MARK(tt))
   MARK(U42(s(z0), x1)) -> c77(A__U42(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
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   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1))
   MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1)))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c74(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2))
   MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1), MARK(zeros))
   MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(cons(z0, z1), x1)) -> c77(A__U42(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1), MARK(tt))
   MARK(U42(s(z0), x1)) -> c77(A__U42(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2


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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1))
   MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c71(MARK(s(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1))
   MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1)))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c74(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2))
   MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1))
   MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1))
   MARK(U42(s(z0), x1)) -> c77(MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
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   MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1))
   MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1)))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c74(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2))
   MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1))
   MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1))
   MARK(U42(s(z0), x1)) -> c77(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1


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

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) by 
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2), MARK(zeros))
   MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(A__U51(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1)))
   MARK(U51(0, x1, x2)) -> c80(A__U51(0, x1, x2), MARK(0))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2), MARK(tt))
   MARK(U51(s(z0), x1, x2)) -> c80(A__U51(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U51(nil, x1, x2)) -> c80(A__U51(nil, x1, x2), MARK(nil))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
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   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1))
   MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1))
   MARK(U42(s(z0), x1)) -> c77(MARK(s(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2), MARK(zeros))
   MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(A__U51(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1)))
   MARK(U51(0, x1, x2)) -> c80(A__U51(0, x1, x2), MARK(0))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2), MARK(tt))
   MARK(U51(s(z0), x1, x2)) -> c80(A__U51(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U51(nil, x1, x2)) -> c80(A__U51(nil, x1, x2), MARK(nil))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
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   MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1))
   MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1))
   MARK(U42(s(z0), x1)) -> c77(MARK(s(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2), MARK(zeros))
   MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(A__U51(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1)))
   MARK(U51(0, x1, x2)) -> c80(A__U51(0, x1, x2), MARK(0))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2), MARK(tt))
   MARK(U51(s(z0), x1, x2)) -> c80(A__U51(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U51(nil, x1, x2)) -> c80(A__U51(nil, x1, x2), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2


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

(119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U51(0, x1, x2)) -> c80(A__U51(0, x1, x2), MARK(0))
   MARK(U51(nil, x1, x2)) -> c80(A__U51(nil, x1, x2), MARK(nil))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
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   MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1))
   MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c71(MARK(s(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1))
   MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1)))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c74(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2))
   MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1))
   MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1))
   MARK(U42(s(z0), x1)) -> c77(MARK(s(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2), MARK(zeros))
   MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(A__U51(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2), MARK(tt))
   MARK(U51(s(z0), x1, x2)) -> c80(A__U51(s(mark(z0)), x1, x2), MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0)))
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   MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1))
   MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1)))
   MARK(U21(tt, x1)) -> c71(A__U21(tt, x1))
   MARK(U21(s(z0), x1)) -> c71(MARK(s(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
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   MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1))
   MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1)))
   MARK(U31(tt, x1)) -> c74(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c74(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2))
   MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1))
   MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1))
   MARK(U42(s(z0), x1)) -> c77(MARK(s(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2), MARK(zeros))
   MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(A__U51(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2), MARK(tt))
   MARK(U51(s(z0), x1, x2)) -> c80(A__U51(s(mark(z0)), x1, x2), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2


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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
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   MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1))
   MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1))
   MARK(U42(s(z0), x1)) -> c77(MARK(s(z0)))
   MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2))
   MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
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   MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1))
   MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1))
   MARK(U42(s(z0), x1)) -> c77(MARK(s(z0)))
   MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2))
   MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1


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

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) by 
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1), MARK(zeros))
   MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(cons(z0, z1), x1)) -> c81(A__U52(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U52(0, x1)) -> c81(A__U52(0, x1), MARK(0))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1), MARK(tt))
   MARK(U52(s(z0), x1)) -> c81(A__U52(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U52(nil, x1)) -> c81(A__U52(nil, x1), MARK(nil))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
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   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2))
   MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1), MARK(zeros))
   MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(cons(z0, z1), x1)) -> c81(A__U52(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U52(0, x1)) -> c81(A__U52(0, x1), MARK(0))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1), MARK(tt))
   MARK(U52(s(z0), x1)) -> c81(A__U52(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U52(nil, x1)) -> c81(A__U52(nil, x1), MARK(nil))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
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   MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1))
   MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1))
   MARK(U42(s(z0), x1)) -> c77(MARK(s(z0)))
   MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2))
   MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1), MARK(zeros))
   MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(cons(z0, z1), x1)) -> c81(A__U52(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U52(0, x1)) -> c81(A__U52(0, x1), MARK(0))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1), MARK(tt))
   MARK(U52(s(z0), x1)) -> c81(A__U52(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U52(nil, x1)) -> c81(A__U52(nil, x1), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2


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

(125) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U52(0, x1)) -> c81(A__U52(0, x1), MARK(0))
   MARK(U52(nil, x1)) -> c81(A__U52(nil, x1), MARK(nil))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(cons(z0, z1), x1)) -> c81(A__U52(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1), MARK(tt))
   MARK(U52(s(z0), x1)) -> c81(A__U52(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
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   MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2))
   MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1), MARK(zeros))
   MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(cons(z0, z1), x1)) -> c81(A__U52(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1), MARK(tt))
   MARK(U52(s(z0), x1)) -> c81(A__U52(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2


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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
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   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
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   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
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   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2))
   MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0)))
   MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1


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

(129) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) by 
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2), MARK(zeros))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(A__U61(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1)))
   MARK(U61(0, x1, x2)) -> c83(A__U61(0, x1, x2), MARK(0))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2), MARK(tt))
   MARK(U61(s(z0), x1, x2)) -> c83(A__U61(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U61(nil, x1, x2)) -> c83(A__U61(nil, x1, x2), MARK(nil))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
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   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
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   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
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   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
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   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
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   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
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   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2), MARK(zeros))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(A__U61(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1)))
   MARK(U61(0, x1, x2)) -> c83(A__U61(0, x1, x2), MARK(0))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2), MARK(tt))
   MARK(U61(s(z0), x1, x2)) -> c83(A__U61(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U61(nil, x1, x2)) -> c83(A__U61(nil, x1, x2), MARK(nil))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
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   MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1))
   MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1))
   MARK(U42(s(z0), x1)) -> c77(MARK(s(z0)))
   MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2))
   MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0)))
   MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2), MARK(zeros))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(A__U61(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1)))
   MARK(U61(0, x1, x2)) -> c83(A__U61(0, x1, x2), MARK(0))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2), MARK(tt))
   MARK(U61(s(z0), x1, x2)) -> c83(A__U61(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U61(nil, x1, x2)) -> c83(A__U61(nil, x1, x2), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2


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

(131) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U61(nil, x1, x2)) -> c83(A__U61(nil, x1, x2), MARK(nil))
   MARK(U61(0, x1, x2)) -> c83(A__U61(0, x1, x2), MARK(0))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
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   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1))
   MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1))
   MARK(U42(s(z0), x1)) -> c77(MARK(s(z0)))
   MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2))
   MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0)))
   MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2), MARK(zeros))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(A__U61(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2), MARK(tt))
   MARK(U61(s(z0), x1, x2)) -> c83(A__U61(s(mark(z0)), x1, x2), MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
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   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(A__U61(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2), MARK(tt))
   MARK(U61(s(z0), x1, x2)) -> c83(A__U61(s(mark(z0)), x1, x2), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2


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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
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   MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2))
   MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1))
   MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1))
   MARK(U42(s(z0), x1)) -> c77(MARK(s(z0)))
   MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2))
   MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0)))
   MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1


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

(135) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) by 
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1), MARK(zeros))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(cons(z0, z1), x1)) -> c84(A__U62(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U62(0, x1)) -> c84(A__U62(0, x1), MARK(0))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1), MARK(tt))
   MARK(U62(s(z0), x1)) -> c84(A__U62(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U62(nil, x1)) -> c84(A__U62(nil, x1), MARK(nil))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
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   MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1), MARK(zeros))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(cons(z0, z1), x1)) -> c84(A__U62(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U62(0, x1)) -> c84(A__U62(0, x1), MARK(0))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1), MARK(tt))
   MARK(U62(s(z0), x1)) -> c84(A__U62(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U62(nil, x1)) -> c84(A__U62(nil, x1), MARK(nil))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
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   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1), MARK(zeros))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(cons(z0, z1), x1)) -> c84(A__U62(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U62(0, x1)) -> c84(A__U62(0, x1), MARK(0))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1), MARK(tt))
   MARK(U62(s(z0), x1)) -> c84(A__U62(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U62(nil, x1)) -> c84(A__U62(nil, x1), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2


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

(137) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U62(nil, x1)) -> c84(A__U62(nil, x1), MARK(nil))
   MARK(U62(0, x1)) -> c84(A__U62(0, x1), 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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
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   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1), MARK(zeros))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(cons(z0, z1), x1)) -> c84(A__U62(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1), MARK(tt))
   MARK(U62(s(z0), x1)) -> c84(A__U62(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
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   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1))
   MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1))
   MARK(U42(s(z0), x1)) -> c77(MARK(s(z0)))
   MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2))
   MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0)))
   MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1), MARK(zeros))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(cons(z0, z1), x1)) -> c84(A__U62(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1), MARK(tt))
   MARK(U62(s(z0), x1)) -> c84(A__U62(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2


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

(139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
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   MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1))
   MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1)))
   MARK(U42(tt, x1)) -> c77(A__U42(tt, x1))
   MARK(U42(s(z0), x1)) -> c77(MARK(s(z0)))
   MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2))
   MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0)))
   MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1))
   MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1))
   MARK(U62(s(z0), x1)) -> c84(MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1))
   MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1))
   MARK(U62(s(z0), x1)) -> c84(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1


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

(141) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) by 
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1), MARK(zeros))
   MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(cons(z0, z1), x1)) -> c86(A__U71(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U71(0, x1)) -> c86(A__U71(0, x1), MARK(0))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1), MARK(tt))
   MARK(U71(s(z0), x1)) -> c86(A__U71(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U71(nil, x1)) -> c86(A__U71(nil, x1), MARK(nil))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2))
   MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0)))
   MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1))
   MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1))
   MARK(U62(s(z0), x1)) -> c84(MARK(s(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1), MARK(zeros))
   MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(cons(z0, z1), x1)) -> c86(A__U71(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U71(0, x1)) -> c86(A__U71(0, x1), MARK(0))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1), MARK(tt))
   MARK(U71(s(z0), x1)) -> c86(A__U71(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U71(nil, x1)) -> c86(A__U71(nil, x1), MARK(nil))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
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   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(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__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
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   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
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   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
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   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
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   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
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   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
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   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
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   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
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   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1))
   MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1))
   MARK(U62(s(z0), x1)) -> c84(MARK(s(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1), MARK(zeros))
   MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(cons(z0, z1), x1)) -> c86(A__U71(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U71(0, x1)) -> c86(A__U71(0, x1), MARK(0))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1), MARK(tt))
   MARK(U71(s(z0), x1)) -> c86(A__U71(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U71(nil, x1)) -> c86(A__U71(nil, x1), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2


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

(143) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U71(nil, x1)) -> c86(A__U71(nil, x1), MARK(nil))
   MARK(U71(0, x1)) -> c86(A__U71(0, x1), MARK(0))

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
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   MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2))
   MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0)))
   MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1))
   MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1))
   MARK(U62(s(z0), x1)) -> c84(MARK(s(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1), MARK(zeros))
   MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(cons(z0, z1), x1)) -> c86(A__U71(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1), MARK(tt))
   MARK(U71(s(z0), x1)) -> c86(A__U71(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
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   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1))
   MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1))
   MARK(U62(s(z0), x1)) -> c84(MARK(s(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1), MARK(zeros))
   MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(cons(z0, z1), x1)) -> c86(A__U71(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1), MARK(tt))
   MARK(U71(s(z0), x1)) -> c86(A__U71(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2


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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2))
   MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1)))
   MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2))
   MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0)))
   MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1))
   MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1))
   MARK(U62(s(z0), x1)) -> c84(MARK(s(z0)))
   MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
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   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1))
   MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1))
   MARK(U62(s(z0), x1)) -> c84(MARK(s(z0)))
   MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1


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

(147) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) by 
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros), MARK(zeros))
   MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(0)) -> c87(A__LENGTH(0), MARK(0))
   MARK(length(tt)) -> c87(A__LENGTH(tt), MARK(tt))
   MARK(length(s(z0))) -> c87(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   MARK(length(nil)) -> c87(A__LENGTH(nil), MARK(nil))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
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   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros), MARK(zeros))
   MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(0)) -> c87(A__LENGTH(0), MARK(0))
   MARK(length(tt)) -> c87(A__LENGTH(tt), MARK(tt))
   MARK(length(s(z0))) -> c87(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   MARK(length(nil)) -> c87(A__LENGTH(nil), MARK(nil))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
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   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros), MARK(zeros))
   MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(0)) -> c87(A__LENGTH(0), MARK(0))
   MARK(length(tt)) -> c87(A__LENGTH(tt), MARK(tt))
   MARK(length(s(z0))) -> c87(A__LENGTH(s(mark(z0))), MARK(s(z0)))
   MARK(length(nil)) -> c87(A__LENGTH(nil), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2


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

(149) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   MARK(length(0)) -> c87(A__LENGTH(0), MARK(0))
   MARK(length(nil)) -> c87(A__LENGTH(nil), MARK(nil))
   MARK(length(tt)) -> c87(A__LENGTH(tt), MARK(tt))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
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   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1))
   MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1))
   MARK(U62(s(z0), x1)) -> c84(MARK(s(z0)))
   MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros), MARK(zeros))
   MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(s(z0))) -> c87(A__LENGTH(s(mark(z0))), MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
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   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
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   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
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   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
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   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1))
   MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1))
   MARK(U62(s(z0), x1)) -> c84(MARK(s(z0)))
   MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros), MARK(zeros))
   MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(s(z0))) -> c87(A__LENGTH(s(mark(z0))), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2


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

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
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   MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1))
   MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1))
   MARK(U62(s(z0), x1)) -> c84(MARK(s(z0)))
   MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
   MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c87(MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1))
   MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1)))
   MARK(U52(tt, x1)) -> c81(A__U52(tt, x1))
   MARK(U52(s(z0), x1)) -> c81(MARK(s(z0)))
   MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0)))
   MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1)))
   MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0)))
   MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0)))
   MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1)))
   MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0)))
   MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0)))
   MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2)))
   MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1)))
   MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0)))
   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1))
   MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1))
   MARK(U62(s(z0), x1)) -> c84(MARK(s(z0)))
   MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
   MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c87(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1


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

(153) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) by 
   MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3), MARK(zeros))
   MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1)))
   MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0)))
   MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1)))
   MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0)))
   MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1)))
   MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0)))
   MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2)))
   MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1)))
   MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0)))
   MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2)))
   MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1)))
   MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0)))
   MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2)))
   MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1)))
   MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0)))
   MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1)))
   MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0)))
   MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3)))
   MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1)))
   MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0)))
   MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0)))
   MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(A__U91(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1)))
   MARK(U91(0, x1, x2, x3)) -> c89(A__U91(0, x1, x2, x3), MARK(0))
   MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3), MARK(tt))
   MARK(U91(s(z0), x1, x2, x3)) -> c89(A__U91(s(mark(z0)), x1, x2, x3), MARK(s(z0)))
   MARK(U91(nil, x1, x2, x3)) -> c89(A__U91(nil, x1, x2, x3), MARK(nil))

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
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   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1))
   MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1))
   MARK(U62(s(z0), x1)) -> c84(MARK(s(z0)))
   MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
   MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c87(MARK(s(z0)))
   MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3), MARK(zeros))
   MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1)))
   MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0)))
   MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1)))
   MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0)))
   MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1)))
   MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0)))
   MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2)))
   MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1)))
   MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0)))
   MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2)))
   MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1)))
   MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0)))
   MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2)))
   MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1)))
   MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0)))
   MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1)))
   MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0)))
   MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3)))
   MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1)))
   MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0)))
   MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0)))
   MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(A__U91(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1)))
   MARK(U91(0, x1, x2, x3)) -> c89(A__U91(0, x1, x2, x3), MARK(0))
   MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3), MARK(tt))
   MARK(U91(s(z0), x1, x2, x3)) -> c89(A__U91(s(mark(z0)), x1, x2, x3), MARK(s(z0)))
   MARK(U91(nil, x1, x2, x3)) -> c89(A__U91(nil, x1, x2, x3), MARK(nil))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
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   MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2)))
   MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1)))
   MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0)))
   MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1)))
   MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0)))
   MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0)))
   MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3)))
   MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1)))
   MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1)))
   MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0)))
   MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0)))
   MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2))
   MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1)))
   MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2))
   MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0)))
   MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1))
   MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1))
   MARK(U62(s(z0), x1)) -> c84(MARK(s(z0)))
   MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
   MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c87(MARK(s(z0)))
   MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3), MARK(zeros))
   MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1)))
   MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0)))
   MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1)))
   MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0)))
   MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1)))
   MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0)))
   MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2)))
   MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1)))
   MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0)))
   MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2)))
   MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1)))
   MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0)))
   MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2)))
   MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1)))
   MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0)))
   MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1)))
   MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0)))
   MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3)))
   MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1)))
   MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0)))
   MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0)))
   MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(A__U91(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1)))
   MARK(U91(0, x1, x2, x3)) -> c89(A__U91(0, x1, x2, x3), MARK(0))
   MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3), MARK(tt))
   MARK(U91(s(z0), x1, x2, x3)) -> c89(A__U91(s(mark(z0)), x1, x2, x3), MARK(s(z0)))
   MARK(U91(nil, x1, x2, x3)) -> c89(A__U91(nil, x1, x2, x3), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2


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

(155) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(U91(nil, x1, x2, x3)) -> c89(A__U91(nil, x1, x2, x3), MARK(nil))
   MARK(U91(0, x1, x2, x3)) -> c89(A__U91(0, x1, x2, x3), MARK(0))

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
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   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
   MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c87(MARK(s(z0)))
   MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3), MARK(zeros))
   MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1)))
   MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0)))
   MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1)))
   MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0)))
   MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1)))
   MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0)))
   MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2)))
   MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1)))
   MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0)))
   MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2)))
   MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1)))
   MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0)))
   MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2)))
   MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1)))
   MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0)))
   MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1)))
   MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0)))
   MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3)))
   MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1)))
   MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0)))
   MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0)))
   MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(A__U91(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1)))
   MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3), MARK(tt))
   MARK(U91(s(z0), x1, x2, x3)) -> c89(A__U91(s(mark(z0)), x1, x2, x3), MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
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   MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1))
   MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1)))
   MARK(U62(tt, x1)) -> c84(A__U62(tt, x1))
   MARK(U62(s(z0), x1)) -> c84(MARK(s(z0)))
   MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
   MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c87(MARK(s(z0)))
   MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3), MARK(zeros))
   MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1)))
   MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0)))
   MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1)))
   MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0)))
   MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1)))
   MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0)))
   MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2)))
   MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1)))
   MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0)))
   MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2)))
   MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1)))
   MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0)))
   MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2)))
   MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1)))
   MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0)))
   MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1)))
   MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0)))
   MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3)))
   MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1)))
   MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0)))
   MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0)))
   MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(A__U91(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1)))
   MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3), MARK(tt))
   MARK(U91(s(z0), x1, x2, x3)) -> c89(A__U91(s(mark(z0)), x1, x2, x3), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2


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

(157) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
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   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c87(MARK(s(z0)))
   MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1)))
   MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0)))
   MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1)))
   MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0)))
   MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1)))
   MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0)))
   MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2)))
   MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1)))
   MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0)))
   MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2)))
   MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1)))
   MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0)))
   MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2)))
   MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1)))
   MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0)))
   MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1)))
   MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0)))
   MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3)))
   MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1)))
   MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0)))
   MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0)))
   MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3))
   MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1)))
   MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3))
   MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
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   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
   MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c87(MARK(s(z0)))
   MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1)))
   MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0)))
   MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1)))
   MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0)))
   MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1)))
   MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0)))
   MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2)))
   MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1)))
   MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0)))
   MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2)))
   MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1)))
   MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0)))
   MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2)))
   MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1)))
   MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0)))
   MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1)))
   MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0)))
   MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3)))
   MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1)))
   MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0)))
   MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0)))
   MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3))
   MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1)))
   MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3))
   MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1


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

(159) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) by 
   MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0))
   MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0))
   MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0))
   MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0))
   MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0))
   MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)), MARK(zeros))
   MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0)))
   MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1)))
   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(cons(z0, z1), x1)) -> c90(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)), MARK(0))
   MARK(take(tt, x1)) -> c90(A__TAKE(tt, mark(x1)), MARK(tt))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(nil, x1)) -> c90(A__TAKE(nil, mark(x1)), MARK(nil))

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
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   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
   MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c87(MARK(s(z0)))
   MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1)))
   MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0)))
   MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1)))
   MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0)))
   MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1)))
   MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0)))
   MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2)))
   MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1)))
   MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0)))
   MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2)))
   MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1)))
   MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0)))
   MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2)))
   MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1)))
   MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0)))
   MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1)))
   MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0)))
   MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3)))
   MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1)))
   MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0)))
   MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0)))
   MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3))
   MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1)))
   MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3))
   MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0)))
   MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0))
   MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0))
   MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0))
   MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0))
   MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0))
   MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)), MARK(zeros))
   MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0)))
   MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1)))
   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(cons(z0, z1), x1)) -> c90(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)), MARK(0))
   MARK(take(tt, x1)) -> c90(A__TAKE(tt, mark(x1)), MARK(tt))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(nil, x1)) -> c90(A__TAKE(nil, mark(x1)), MARK(nil))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
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   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
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   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
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   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
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   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
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   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
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   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
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   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
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   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
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   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
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   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
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   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
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   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
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   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
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   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
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   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
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   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
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   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
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   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
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   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
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   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
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   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
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   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
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   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
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   MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3))
   MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1)))
   MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3))
   MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0)))
   MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0))
   MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0))
   MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0))
   MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0))
   MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0))
   MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)), MARK(zeros))
   MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0)))
   MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1)))
   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(cons(z0, z1), x1)) -> c90(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)), MARK(0))
   MARK(take(tt, x1)) -> c90(A__TAKE(tt, mark(x1)), MARK(tt))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(nil, x1)) -> c90(A__TAKE(nil, mark(x1)), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2


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

(161) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(take(tt, x1)) -> c90(A__TAKE(tt, mark(x1)), MARK(tt))
   MARK(take(nil, x1)) -> c90(A__TAKE(nil, mark(x1)), MARK(nil))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
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   MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0))
   MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0))
   MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0))
   MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0))
   MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0))
   MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)), MARK(zeros))
   MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0)))
   MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1)))
   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(cons(z0, z1), x1)) -> c90(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)), MARK(0))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
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   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
   MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c87(MARK(s(z0)))
   MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1)))
   MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0)))
   MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1)))
   MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0)))
   MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1)))
   MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0)))
   MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2)))
   MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1)))
   MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0)))
   MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2)))
   MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1)))
   MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0)))
   MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2)))
   MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1)))
   MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0)))
   MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1)))
   MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0)))
   MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3)))
   MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1)))
   MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0)))
   MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0)))
   MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3))
   MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1)))
   MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3))
   MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0)))
   MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0))
   MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0))
   MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0))
   MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0))
   MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0))
   MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)), MARK(zeros))
   MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0)))
   MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1)))
   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(cons(z0, z1), x1)) -> c90(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)), MARK(0))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2


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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
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   MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1))
   MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1)))
   MARK(U71(tt, x1)) -> c86(A__U71(tt, x1))
   MARK(U71(s(z0), x1)) -> c86(MARK(s(z0)))
   MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(length(zeros)) -> c87(A__LENGTH(a__zeros))
   MARK(length(s(z0))) -> c87(MARK(s(z0)))
   MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1)))
   MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0)))
   MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0)))
   MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1)))
   MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0)))
   MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0)))
   MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1)))
   MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0)))
   MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2)))
   MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1)))
   MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0)))
   MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0)))
   MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2)))
   MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1)))
   MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0)))
   MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2)))
   MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1)))
   MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0)))
   MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1)))
   MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0)))
   MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3)))
   MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1)))
   MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0)))
   MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0)))
   MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3))
   MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1)))
   MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3))
   MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0)))
   MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0))
   MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0))
   MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0))
   MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0))
   MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0))
   MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0)))
   MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1)))
   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2)))
   MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1)))
   MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0)))
   MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1)))
   MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0)))
   MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0)))
   MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3)))
   MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1)))
   MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1)))
   MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0)))
   MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0)))
   MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3))
   MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1)))
   MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3))
   MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0)))
   MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0))
   MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0))
   MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0))
   MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0))
   MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0))
   MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0)))
   MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1)))
   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1


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

(165) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) by 
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros), MARK(zeros))
   MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0), MARK(0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt), MARK(tt))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil), MARK(nil))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c91(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(tt, x1)) -> c91(A__TAKE(tt, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(nil, x1)) -> c91(A__TAKE(nil, mark(x1)), MARK(x1))

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
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   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0), MARK(0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt), MARK(tt))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil), MARK(nil))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c91(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(tt, x1)) -> c91(A__TAKE(tt, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(nil, x1)) -> c91(A__TAKE(nil, mark(x1)), MARK(x1))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
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   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0), MARK(0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt), MARK(tt))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil), MARK(nil))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(cons(z0, z1), x1)) -> c91(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(tt, x1)) -> c91(A__TAKE(tt, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(nil, x1)) -> c91(A__TAKE(nil, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2


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

(167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 7 trailing tuple parts
----------------------------------------

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
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   MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0)))
   MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1)))
   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
   MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
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   MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1)))
   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
   MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1


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

(169) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) by 
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1), MARK(zeros))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(cons(z0, z1), x1)) -> c92(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(and(0, x1)) -> c92(A__AND(0, x1), MARK(0))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1), MARK(tt))
   MARK(and(s(z0), x1)) -> c92(A__AND(s(mark(z0)), x1), MARK(s(z0)))
   MARK(and(nil, x1)) -> c92(A__AND(nil, x1), MARK(nil))

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

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
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   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1), MARK(zeros))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(cons(z0, z1), x1)) -> c92(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(and(0, x1)) -> c92(A__AND(0, x1), MARK(0))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1), MARK(tt))
   MARK(and(s(z0), x1)) -> c92(A__AND(s(mark(z0)), x1), MARK(s(z0)))
   MARK(and(nil, x1)) -> c92(A__AND(nil, x1), MARK(nil))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
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   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1), MARK(zeros))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(cons(z0, z1), x1)) -> c92(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(and(0, x1)) -> c92(A__AND(0, x1), MARK(0))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1), MARK(tt))
   MARK(and(s(z0), x1)) -> c92(A__AND(s(mark(z0)), x1), MARK(s(z0)))
   MARK(and(nil, x1)) -> c92(A__AND(nil, x1), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2


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

(171) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(and(0, x1)) -> c92(A__AND(0, x1), MARK(0))
   MARK(and(nil, x1)) -> c92(A__AND(nil, x1), MARK(nil))

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
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   MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0))
   MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0))
   MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0))
   MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0))
   MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0)))
   MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1)))
   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
   MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1), MARK(zeros))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(cons(z0, z1), x1)) -> c92(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1), MARK(tt))
   MARK(and(s(z0), x1)) -> c92(A__AND(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
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   MARK(and(s(z0), x1)) -> c92(A__AND(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2


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

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

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
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   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
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   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
   MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1


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

(175) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) by 
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__AND(isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))

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

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
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   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__AND(isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
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   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__AND(isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2


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

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

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
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   MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0))
   MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0))
   MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0))
   MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0)))
   MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1)))
   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
   MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
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   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
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   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
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   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
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   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
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   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
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   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
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   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
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   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
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   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
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   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
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   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
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   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
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   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
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   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
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   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
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   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
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   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
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   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0)))
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   MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
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   MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3))
   MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1)))
   MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3))
   MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0)))
   MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0))
   MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0))
   MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0))
   MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0))
   MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0))
   MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0))
   MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0))
   MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0))
   MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0))
   MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0))
   MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0)))
   MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1)))
   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
   MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1


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

(179) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) by 
   A__U41(tt, length(z1), x1) -> c14(A__U42(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1)))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))

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

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
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   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(z1), x1) -> c14(A__U42(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1)))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
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   MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0)))
   MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1)))
   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
   MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(z1), x1) -> c14(A__U42(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1)))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1


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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
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   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
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   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1


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

(183) 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)))

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

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
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   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(z1), x1) -> c14(A__U42(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
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   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(z1), x1) -> c14(A__U42(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2


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

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

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
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   MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0))
   MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0))
   MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0))
   MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0))
   MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0))
   MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0))
   MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0))
   MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0))
   MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0))
   MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0))
   MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0))
   MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0))
   MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0))
   MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0))
   MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0))
   MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0)))
   MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1)))
   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
   MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
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   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2


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

(187) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) by 
   A__U51(tt, length(z1), x1) -> c20(A__U52(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))

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

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
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   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
   MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(z1), x1) -> c20(A__U52(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(z1), x1) -> c20(A__U52(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2


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

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

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
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   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
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   MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0)))
   MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1)))
   MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0)))
   MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0)))
   MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1)))
   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
   MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2


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

(191) 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)))

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

(192)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
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   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(z1), x1) -> c20(A__U52(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
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   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
   MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(z1), x1) -> c20(A__U52(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2


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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
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   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
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   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
   MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2


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

(195) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) by 
   A__U61(tt, length(z1), x1) -> c26(A__U62(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))

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

(196)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
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   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(z1), x1) -> c26(A__U62(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
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   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
   MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(z1), x1) -> c26(A__U62(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2


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

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

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
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   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
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   MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0)))
   MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0)))
   MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2)))
   MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1)))
   MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0)))
   MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2)))
   MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1)))
   MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0)))
   MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1)))
   MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0)))
   MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0)))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1)))
   MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1)))
   MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0)))
   MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0)))
   MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)))
   MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1)))
   MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)))
   MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2


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

(199) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) by 
   A__U61(tt, s(z1), x1) -> c26(A__U62(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))

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

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
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   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
   A__U61(tt, s(z1), x1) -> c26(A__U62(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
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   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
   A__U61(tt, s(z1), x1) -> c26(A__U62(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2


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

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

(202)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
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   MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0)))
   MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0)))
   MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0)))
   MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0)))
   MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0)))
   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
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   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2


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

(203) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) by 
   A__U71(tt, U11(x0, z1)) -> c32(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1)))
   A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1)))
   A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1)))
   A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1)))
   A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1)))
   A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1)))
   A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1)))
   A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1)))
   A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1)))
   A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1)))
   A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1)))
   A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1)))
   A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1)))
   A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1)))
   A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1)))
   A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1)))
   A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1)))
   A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1)))
   A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1)))
   A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1)))
   A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1)))
   A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1)))
   A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1)))
   A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1)))

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

(204)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
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   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1)))
   A__U71(tt, U11(x0, z1)) -> c32(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1)))
   A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1)))
   A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1)))
   A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1)))
   A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1)))
   A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1)))
   A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1)))
   A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1)))
   A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1)))
   A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1)))
   A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1)))
   A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1)))
   A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1)))
   A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1)))
   A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1)))
   A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1)))
   A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1)))
   A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1)))
   A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1)))
   A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1)))
   A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1)))
   A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1)))
   A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1)))
   A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
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   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1)))
   A__U71(tt, U11(x0, z1)) -> c32(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1)))
   A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1)))
   A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1)))
   A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1)))
   A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1)))
   A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1)))
   A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1)))
   A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1)))
   A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1)))
   A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1)))
   A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1)))
   A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1)))
   A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1)))
   A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1)))
   A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1)))
   A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1)))
   A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1)))
   A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1)))
   A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1)))
   A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1)))
   A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1)))
   A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1)))
   A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1)))
   A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2


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(205) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
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   MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0)))
   MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0)))
   MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0)))
   MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0)))
   MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1)))
   MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0)))
   MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1))
   MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1))
   MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1))
   MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1)))
   A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1)))
   A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1)))
   A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1)))
   A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1)))
   A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1)))
   A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1)))
   A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1)))
   A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1)))
   A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1)))
   A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1)))
   A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1)))
   A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1)))
   A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1)))
   A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1)))
   A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1)))
   A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1)))
   A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1)))
   A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1)))
   A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1)))
   A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1)))
   A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1)))
   A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1)))
   A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)))
   A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0)))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
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   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1)))
   A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1)))
   A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1)))
   A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1)))
   A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1)))
   A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1)))
   A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1)))
   A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1)))
   A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1)))
   A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1)))
   A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1)))
   A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1)))
   A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1)))
   A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1)))
   A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1)))
   A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1)))
   A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1)))
   A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1)))
   A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1)))
   A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1)))
   A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1)))
   A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1)))
   A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1)))
   A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)))
   A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2


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

(207) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) by 
   A__U71(tt, U12(x0)) -> c32(A__LENGTH(U12(mark(x0))), MARK(U12(x0)))
   A__U71(tt, U12(zeros)) -> c32(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros)))
   A__U71(tt, U12(U11(z0, z1))) -> c32(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U71(tt, U12(U12(z0))) -> c32(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U71(tt, U12(isNatList(z0))) -> c32(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0))))
   A__U71(tt, U12(U21(z0, z1))) -> c32(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1))))
   A__U71(tt, U12(U22(z0))) -> c32(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0))))
   A__U71(tt, U12(isNat(z0))) -> c32(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U71(tt, U12(U31(z0, z1))) -> c32(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U71(tt, U12(U32(z0))) -> c32(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0))))
   A__U71(tt, U12(U41(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U71(tt, U12(U42(z0, z1))) -> c32(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1))))
   A__U71(tt, U12(U43(z0))) -> c32(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0))))
   A__U71(tt, U12(isNatIList(z0))) -> c32(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0))))
   A__U71(tt, U12(U51(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2))))
   A__U71(tt, U12(U52(z0, z1))) -> c32(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1))))
   A__U71(tt, U12(U53(z0))) -> c32(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0))))
   A__U71(tt, U12(U61(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U61(mark(z0), z1, z2))), MARK(U12(U61(z0, z1, z2))))
   A__U71(tt, U12(U62(z0, z1))) -> c32(A__LENGTH(a__U12(a__U62(mark(z0), z1))), MARK(U12(U62(z0, z1))))
   A__U71(tt, U12(U63(z0))) -> c32(A__LENGTH(a__U12(a__U63(mark(z0)))), MARK(U12(U63(z0))))
   A__U71(tt, U12(U71(z0, z1))) -> c32(A__LENGTH(a__U12(a__U71(mark(z0), z1))), MARK(U12(U71(z0, z1))))
   A__U71(tt, U12(length(z0))) -> c32(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0))))
   A__U71(tt, U12(U81(z0))) -> c32(A__LENGTH(a__U12(a__U81(mark(z0)))), MARK(U12(U81(z0))))
   A__U71(tt, U12(U91(z0, z1, z2, z3))) -> c32(A__LENGTH(a__U12(a__U91(mark(z0), z1, z2, z3))), MARK(U12(U91(z0, z1, z2, z3))))
   A__U71(tt, U12(take(z0, z1))) -> c32(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)))), MARK(U12(take(z0, z1))))
   A__U71(tt, U12(and(z0, z1))) -> c32(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1))))
   A__U71(tt, U12(isNatIListKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0))))
   A__U71(tt, U12(isNatKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0))))
   A__U71(tt, U12(cons(z0, z1))) -> c32(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1))))
   A__U71(tt, U12(0)) -> c32(A__LENGTH(a__U12(0)), MARK(U12(0)))
   A__U71(tt, U12(tt)) -> c32(A__LENGTH(a__U12(tt)), MARK(U12(tt)))
   A__U71(tt, U12(s(z0))) -> c32(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U71(tt, U12(nil)) -> c32(A__LENGTH(a__U12(nil)), MARK(U12(nil)))
   A__U71(tt, U12(x0)) -> c32(MARK(U12(x0)))

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

(208)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
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   MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1))
   MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1)))
   A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1)))
   A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1)))
   A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1)))
   A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1)))
   A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1)))
   A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1)))
   A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1)))
   A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1)))
   A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1)))
   A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1)))
   A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1)))
   A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1)))
   A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1)))
   A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1)))
   A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1)))
   A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1)))
   A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1)))
   A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1)))
   A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1)))
   A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1)))
   A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1)))
   A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1)))
   A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)))
   A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)))
   A__U71(tt, U12(x0)) -> c32(A__LENGTH(U12(mark(x0))), MARK(U12(x0)))
   A__U71(tt, U12(zeros)) -> c32(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros)))
   A__U71(tt, U12(U11(z0, z1))) -> c32(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U71(tt, U12(U12(z0))) -> c32(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U71(tt, U12(isNatList(z0))) -> c32(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0))))
   A__U71(tt, U12(U21(z0, z1))) -> c32(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1))))
   A__U71(tt, U12(U22(z0))) -> c32(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0))))
   A__U71(tt, U12(isNat(z0))) -> c32(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U71(tt, U12(U31(z0, z1))) -> c32(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U71(tt, U12(U32(z0))) -> c32(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0))))
   A__U71(tt, U12(U41(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U71(tt, U12(U42(z0, z1))) -> c32(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1))))
   A__U71(tt, U12(U43(z0))) -> c32(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0))))
   A__U71(tt, U12(isNatIList(z0))) -> c32(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0))))
   A__U71(tt, U12(U51(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2))))
   A__U71(tt, U12(U52(z0, z1))) -> c32(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1))))
   A__U71(tt, U12(U53(z0))) -> c32(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0))))
   A__U71(tt, U12(U61(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U61(mark(z0), z1, z2))), MARK(U12(U61(z0, z1, z2))))
   A__U71(tt, U12(U62(z0, z1))) -> c32(A__LENGTH(a__U12(a__U62(mark(z0), z1))), MARK(U12(U62(z0, z1))))
   A__U71(tt, U12(U63(z0))) -> c32(A__LENGTH(a__U12(a__U63(mark(z0)))), MARK(U12(U63(z0))))
   A__U71(tt, U12(U71(z0, z1))) -> c32(A__LENGTH(a__U12(a__U71(mark(z0), z1))), MARK(U12(U71(z0, z1))))
   A__U71(tt, U12(length(z0))) -> c32(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0))))
   A__U71(tt, U12(U81(z0))) -> c32(A__LENGTH(a__U12(a__U81(mark(z0)))), MARK(U12(U81(z0))))
   A__U71(tt, U12(U91(z0, z1, z2, z3))) -> c32(A__LENGTH(a__U12(a__U91(mark(z0), z1, z2, z3))), MARK(U12(U91(z0, z1, z2, z3))))
   A__U71(tt, U12(take(z0, z1))) -> c32(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)))), MARK(U12(take(z0, z1))))
   A__U71(tt, U12(and(z0, z1))) -> c32(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1))))
   A__U71(tt, U12(isNatIListKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0))))
   A__U71(tt, U12(isNatKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0))))
   A__U71(tt, U12(cons(z0, z1))) -> c32(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1))))
   A__U71(tt, U12(0)) -> c32(A__LENGTH(a__U12(0)), MARK(U12(0)))
   A__U71(tt, U12(tt)) -> c32(A__LENGTH(a__U12(tt)), MARK(U12(tt)))
   A__U71(tt, U12(s(z0))) -> c32(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U71(tt, U12(nil)) -> c32(A__LENGTH(a__U12(nil)), MARK(U12(nil)))
   A__U71(tt, U12(x0)) -> c32(MARK(U12(x0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
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   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
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   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
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   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
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   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
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   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
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   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
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   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
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   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
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   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1)))
   A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1)))
   A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1)))
   A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1)))
   A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1)))
   A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1)))
   A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1)))
   A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1)))
   A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1)))
   A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1)))
   A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1)))
   A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1)))
   A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1)))
   A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1)))
   A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1)))
   A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1)))
   A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1)))
   A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1)))
   A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1)))
   A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1)))
   A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1)))
   A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1)))
   A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1)))
   A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)))
   A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)))
   A__U71(tt, U12(x0)) -> c32(A__LENGTH(U12(mark(x0))), MARK(U12(x0)))
   A__U71(tt, U12(zeros)) -> c32(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros)))
   A__U71(tt, U12(U11(z0, z1))) -> c32(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U71(tt, U12(U12(z0))) -> c32(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U71(tt, U12(isNatList(z0))) -> c32(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0))))
   A__U71(tt, U12(U21(z0, z1))) -> c32(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1))))
   A__U71(tt, U12(U22(z0))) -> c32(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0))))
   A__U71(tt, U12(isNat(z0))) -> c32(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U71(tt, U12(U31(z0, z1))) -> c32(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U71(tt, U12(U32(z0))) -> c32(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0))))
   A__U71(tt, U12(U41(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U71(tt, U12(U42(z0, z1))) -> c32(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1))))
   A__U71(tt, U12(U43(z0))) -> c32(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0))))
   A__U71(tt, U12(isNatIList(z0))) -> c32(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0))))
   A__U71(tt, U12(U51(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2))))
   A__U71(tt, U12(U52(z0, z1))) -> c32(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1))))
   A__U71(tt, U12(U53(z0))) -> c32(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0))))
   A__U71(tt, U12(U61(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U61(mark(z0), z1, z2))), MARK(U12(U61(z0, z1, z2))))
   A__U71(tt, U12(U62(z0, z1))) -> c32(A__LENGTH(a__U12(a__U62(mark(z0), z1))), MARK(U12(U62(z0, z1))))
   A__U71(tt, U12(U63(z0))) -> c32(A__LENGTH(a__U12(a__U63(mark(z0)))), MARK(U12(U63(z0))))
   A__U71(tt, U12(U71(z0, z1))) -> c32(A__LENGTH(a__U12(a__U71(mark(z0), z1))), MARK(U12(U71(z0, z1))))
   A__U71(tt, U12(length(z0))) -> c32(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0))))
   A__U71(tt, U12(U81(z0))) -> c32(A__LENGTH(a__U12(a__U81(mark(z0)))), MARK(U12(U81(z0))))
   A__U71(tt, U12(U91(z0, z1, z2, z3))) -> c32(A__LENGTH(a__U12(a__U91(mark(z0), z1, z2, z3))), MARK(U12(U91(z0, z1, z2, z3))))
   A__U71(tt, U12(take(z0, z1))) -> c32(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)))), MARK(U12(take(z0, z1))))
   A__U71(tt, U12(and(z0, z1))) -> c32(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1))))
   A__U71(tt, U12(isNatIListKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0))))
   A__U71(tt, U12(isNatKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0))))
   A__U71(tt, U12(cons(z0, z1))) -> c32(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1))))
   A__U71(tt, U12(0)) -> c32(A__LENGTH(a__U12(0)), MARK(U12(0)))
   A__U71(tt, U12(tt)) -> c32(A__LENGTH(a__U12(tt)), MARK(U12(tt)))
   A__U71(tt, U12(s(z0))) -> c32(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U71(tt, U12(nil)) -> c32(A__LENGTH(a__U12(nil)), MARK(U12(nil)))
   A__U71(tt, U12(x0)) -> c32(MARK(U12(x0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2


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

(209) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
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   MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1))
   MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1))
   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1)))
   A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1)))
   A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1)))
   A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1)))
   A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1)))
   A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1)))
   A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1)))
   A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1)))
   A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1)))
   A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1)))
   A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1)))
   A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1)))
   A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1)))
   A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1)))
   A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1)))
   A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1)))
   A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1)))
   A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1)))
   A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1)))
   A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1)))
   A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1)))
   A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1)))
   A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1)))
   A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)))
   A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)))
   A__U71(tt, U12(zeros)) -> c32(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros)))
   A__U71(tt, U12(U11(z0, z1))) -> c32(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U71(tt, U12(U12(z0))) -> c32(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U71(tt, U12(isNatList(z0))) -> c32(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0))))
   A__U71(tt, U12(U21(z0, z1))) -> c32(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1))))
   A__U71(tt, U12(U22(z0))) -> c32(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0))))
   A__U71(tt, U12(isNat(z0))) -> c32(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U71(tt, U12(U31(z0, z1))) -> c32(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U71(tt, U12(U32(z0))) -> c32(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0))))
   A__U71(tt, U12(U41(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U71(tt, U12(U42(z0, z1))) -> c32(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1))))
   A__U71(tt, U12(U43(z0))) -> c32(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0))))
   A__U71(tt, U12(isNatIList(z0))) -> c32(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0))))
   A__U71(tt, U12(U51(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2))))
   A__U71(tt, U12(U52(z0, z1))) -> c32(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1))))
   A__U71(tt, U12(U53(z0))) -> c32(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0))))
   A__U71(tt, U12(U61(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U61(mark(z0), z1, z2))), MARK(U12(U61(z0, z1, z2))))
   A__U71(tt, U12(U62(z0, z1))) -> c32(A__LENGTH(a__U12(a__U62(mark(z0), z1))), MARK(U12(U62(z0, z1))))
   A__U71(tt, U12(U63(z0))) -> c32(A__LENGTH(a__U12(a__U63(mark(z0)))), MARK(U12(U63(z0))))
   A__U71(tt, U12(U71(z0, z1))) -> c32(A__LENGTH(a__U12(a__U71(mark(z0), z1))), MARK(U12(U71(z0, z1))))
   A__U71(tt, U12(length(z0))) -> c32(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0))))
   A__U71(tt, U12(U81(z0))) -> c32(A__LENGTH(a__U12(a__U81(mark(z0)))), MARK(U12(U81(z0))))
   A__U71(tt, U12(U91(z0, z1, z2, z3))) -> c32(A__LENGTH(a__U12(a__U91(mark(z0), z1, z2, z3))), MARK(U12(U91(z0, z1, z2, z3))))
   A__U71(tt, U12(take(z0, z1))) -> c32(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)))), MARK(U12(take(z0, z1))))
   A__U71(tt, U12(and(z0, z1))) -> c32(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1))))
   A__U71(tt, U12(isNatIListKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0))))
   A__U71(tt, U12(isNatKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0))))
   A__U71(tt, U12(cons(z0, z1))) -> c32(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1))))
   A__U71(tt, U12(0)) -> c32(A__LENGTH(a__U12(0)), MARK(U12(0)))
   A__U71(tt, U12(tt)) -> c32(A__LENGTH(a__U12(tt)), MARK(U12(tt)))
   A__U71(tt, U12(s(z0))) -> c32(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U71(tt, U12(nil)) -> c32(A__LENGTH(a__U12(nil)), MARK(U12(nil)))
   A__U71(tt, U12(x0)) -> c32(MARK(U12(x0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0)))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
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   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1)))
   A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1)))
   A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1)))
   A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1)))
   A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1)))
   A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1)))
   A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1)))
   A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1)))
   A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1)))
   A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1)))
   A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1)))
   A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1)))
   A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1)))
   A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1)))
   A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1)))
   A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1)))
   A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1)))
   A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1)))
   A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1)))
   A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1)))
   A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1)))
   A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1)))
   A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1)))
   A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)))
   A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)))
   A__U71(tt, U12(zeros)) -> c32(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros)))
   A__U71(tt, U12(U11(z0, z1))) -> c32(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U71(tt, U12(U12(z0))) -> c32(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U71(tt, U12(isNatList(z0))) -> c32(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0))))
   A__U71(tt, U12(U21(z0, z1))) -> c32(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1))))
   A__U71(tt, U12(U22(z0))) -> c32(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0))))
   A__U71(tt, U12(isNat(z0))) -> c32(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U71(tt, U12(U31(z0, z1))) -> c32(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U71(tt, U12(U32(z0))) -> c32(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0))))
   A__U71(tt, U12(U41(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U71(tt, U12(U42(z0, z1))) -> c32(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1))))
   A__U71(tt, U12(U43(z0))) -> c32(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0))))
   A__U71(tt, U12(isNatIList(z0))) -> c32(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0))))
   A__U71(tt, U12(U51(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2))))
   A__U71(tt, U12(U52(z0, z1))) -> c32(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1))))
   A__U71(tt, U12(U53(z0))) -> c32(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0))))
   A__U71(tt, U12(U61(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U61(mark(z0), z1, z2))), MARK(U12(U61(z0, z1, z2))))
   A__U71(tt, U12(U62(z0, z1))) -> c32(A__LENGTH(a__U12(a__U62(mark(z0), z1))), MARK(U12(U62(z0, z1))))
   A__U71(tt, U12(U63(z0))) -> c32(A__LENGTH(a__U12(a__U63(mark(z0)))), MARK(U12(U63(z0))))
   A__U71(tt, U12(U71(z0, z1))) -> c32(A__LENGTH(a__U12(a__U71(mark(z0), z1))), MARK(U12(U71(z0, z1))))
   A__U71(tt, U12(length(z0))) -> c32(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0))))
   A__U71(tt, U12(U81(z0))) -> c32(A__LENGTH(a__U12(a__U81(mark(z0)))), MARK(U12(U81(z0))))
   A__U71(tt, U12(U91(z0, z1, z2, z3))) -> c32(A__LENGTH(a__U12(a__U91(mark(z0), z1, z2, z3))), MARK(U12(U91(z0, z1, z2, z3))))
   A__U71(tt, U12(take(z0, z1))) -> c32(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)))), MARK(U12(take(z0, z1))))
   A__U71(tt, U12(and(z0, z1))) -> c32(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1))))
   A__U71(tt, U12(isNatIListKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0))))
   A__U71(tt, U12(isNatKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0))))
   A__U71(tt, U12(cons(z0, z1))) -> c32(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1))))
   A__U71(tt, U12(0)) -> c32(A__LENGTH(a__U12(0)), MARK(U12(0)))
   A__U71(tt, U12(tt)) -> c32(A__LENGTH(a__U12(tt)), MARK(U12(tt)))
   A__U71(tt, U12(s(z0))) -> c32(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U71(tt, U12(nil)) -> c32(A__LENGTH(a__U12(nil)), MARK(U12(nil)))
   A__U71(tt, U12(x0)) -> c32(MARK(U12(x0)))
K tuples:none
Defined Rule Symbols:   a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2


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

(211) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) by 
   A__U71(tt, isNatList(nil)) -> c32(A__LENGTH(tt), MARK(isNatList(nil)))
   A__U71(tt, isNatList(cons(z0, z1))) -> c32(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1))))
   A__U71(tt, isNatList(take(z0, z1))) -> c32(A__LENGTH(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(take(z0, z1))))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(isNatList(z0)), MARK(isNatList(z0)))

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

(212)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__zeros -> cons(0, zeros)
   a__zeros -> zeros
   a__U11(tt, z0) -> a__U12(a__isNatList(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt, z0) -> a__U22(a__isNat(z0))
   a__U21(z0, z1) -> U21(z0, z1)
   a__U22(tt) -> tt
   a__U22(z0) -> U22(z0)
   a__U31(tt, z0) -> a__U32(a__isNatList(z0))
   a__U31(z0, z1) -> U31(z0, z1)
   a__U32(tt) -> tt
   a__U32(z0) -> U32(z0)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0) -> a__U43(a__isNatIList(z0))
   a__U42(z0, z1) -> U42(z0, z1)
   a__U43(tt) -> tt
   a__U43(z0) -> U43(z0)
   a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1)
   a__U51(z0, z1, z2) -> U51(z0, z1, z2)
   a__U52(tt, z0) -> a__U53(a__isNatList(z0))
   a__U52(z0, z1) -> U52(z0, z1)
   a__U53(tt) -> tt
   a__U53(z0) -> U53(z0)
   a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
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   MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1))
   MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros))
   MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0))
   MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt))
   MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil))
   MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1))
   MARK(take(tt, x1)) -> c91(MARK(x1))
   MARK(take(nil, x1)) -> c91(MARK(x1))
   MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1)))
   A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1)))
   A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1)))
   A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1)))
   A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1)))
   A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1)))
   A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1)))
   A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1)))
   A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1)))
   A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1)))
   A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1)))
   A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1)))
   A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1)))
   A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1)))
   A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1)))
   A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1)))
   A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1)))
   A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1)))
   A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1)))
   A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1)))
   A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1)))
   A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1)))
   A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1)))
   A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)))
   A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)))
   A__U71(tt, U12(zeros)) -> c32(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros)))
   A__U71(tt, U12(U11(z0, z1))) -> c32(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U71(tt, U12(U12(z0))) -> c32(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U71(tt, U12(isNatList(z0))) -> c32(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0))))
   A__U71(tt, U12(U21(z0, z1))) -> c32(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1))))
   A__U71(tt, U12(U22(z0))) -> c32(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0))))
   A__U71(tt, U12(isNat(z0))) -> c32(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U71(tt, U12(U31(z0, z1))) -> c32(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U71(tt, U12(U32(z0))) -> c32(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0))))
   A__U71(tt, U12(U41(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U71(tt, U12(U42(z0, z1))) -> c32(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1))))
   A__U71(tt, U12(U43(z0))) -> c32(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0))))
   A__U71(tt, U12(isNatIList(z0))) -> c32(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0))))
   A__U71(tt, U12(U51(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2))))
   A__U71(tt, U12(U52(z0, z1))) -> c32(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1))))
   A__U71(tt, U12(U53(z0))) -> c32(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0))))
   A__U71(tt, U12(U61(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U61(mark(z0), z1, z2))), MARK(U12(U61(z0, z1, z2))))
   A__U71(tt, U12(U62(z0, z1))) -> c32(A__LENGTH(a__U12(a__U62(mark(z0), z1))), MARK(U12(U62(z0, z1))))
   A__U71(tt, U12(U63(z0))) -> c32(A__LENGTH(a__U12(a__U63(mark(z0)))), MARK(U12(U63(z0))))
   A__U71(tt, U12(U71(z0, z1))) -> c32(A__LENGTH(a__U12(a__U71(mark(z0), z1))), MARK(U12(U71(z0, z1))))
   A__U71(tt, U12(length(z0))) -> c32(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0))))
   A__U71(tt, U12(U81(z0))) -> c32(A__LENGTH(a__U12(a__U81(mark(z0)))), MARK(U12(U81(z0))))
   A__U71(tt, U12(U91(z0, z1, z2, z3))) -> c32(A__LENGTH(a__U12(a__U91(mark(z0), z1, z2, z3))), MARK(U12(U91(z0, z1, z2, z3))))
   A__U71(tt, U12(take(z0, z1))) -> c32(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)))), MARK(U12(take(z0, z1))))
   A__U71(tt, U12(and(z0, z1))) -> c32(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1))))
   A__U71(tt, U12(isNatIListKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0))))
   A__U71(tt, U12(isNatKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0))))
   A__U71(tt, U12(cons(z0, z1))) -> c32(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1))))
   A__U71(tt, U12(0)) -> c32(A__LENGTH(a__U12(0)), MARK(U12(0)))
   A__U71(tt, U12(tt)) -> c32(A__LENGTH(a__U12(tt)), MARK(U12(tt)))
   A__U71(tt, U12(s(z0))) -> c32(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U71(tt, U12(nil)) -> c32(A__LENGTH(a__U12(nil)), MARK(U12(nil)))
   A__U71(tt, U12(x0)) -> c32(MARK(U12(x0)))
   A__U71(tt, isNatList(nil)) -> c32(A__LENGTH(tt), MARK(isNatList(nil)))
   A__U71(tt, isNatList(cons(z0, z1))) -> c32(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1))))
   A__U71(tt, isNatList(take(z0, z1))) -> c32(A__LENGTH(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(take(z0, z1))))
   A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(isNatList(z0)), MARK(isNatList(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
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   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
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   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
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   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
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   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
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   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
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   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
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   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
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   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
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   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
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   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
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   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
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   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
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   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
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   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
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   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
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   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
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   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
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   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
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   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
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   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
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   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1)))
   A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1)))
   A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1)))
   A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1)))
   A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1)))
   A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1)))
   A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1)))
   A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1)))
   A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1)))
   A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1)))
   A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1)))
   A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1)))
   A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1)))
   A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1)))
   A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1)))
   A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1)))
   A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1)))
   A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1)))
   A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1)))
   A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1)))
   A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1)))
   A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1)))
   A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1)))
   A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)))
   A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)))
   A__U71(tt, U12(zeros)) -> c32(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros)))
   A__U71(tt, U12(U11(z0, z1))) -> c32(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U71(tt, U12(U12(z0))) -> c32(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U71(tt, U12(isNatList(z0))) -> c32(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0))))
   A__U71(tt, U12(U21(z0, z1))) -> c32(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1))))
   A__U71(tt, U12(U22(z0))) -> c32(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0))))
   A__U71(tt, U12(isNat(z0))) -> c32(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U71(tt, U12(U31(z0, z1))) -> c32(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U71(tt, U12(U32(z0))) -> c32(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0))))
   A__U71(tt, U12(U41(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U71(tt, U12(U42(z0, z1))) -> c32(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1))))
   A__U71(tt, U12(U43(z0))) -> c32(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0))))
   A__U71(tt, U12(isNatIList(z0))) -> c32(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0))))
   A__U71(tt, U12(U51(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2))))
   A__U71(tt, U12(U52(z0, z1))) -> c32(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1))))
   A__U71(tt, U12(U53(z0))) -> c32(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0))))
   A__U71(tt, U12(U61(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U61(mark(z0), z1, z2))), MARK(U12(U61(z0, z1, z2))))
   A__U71(tt, U12(U62(z0, z1))) -> c32(A__LENGTH(a__U12(a__U62(mark(z0), z1))), MARK(U12(U62(z0, z1))))
   A__U71(tt, U12(U63(z0))) -> c32(A__LENGTH(a__U12(a__U63(mark(z0)))), MARK(U12(U63(z0))))
   A__U71(tt, U12(U71(z0, z1))) -> c32(A__LENGTH(a__U12(a__U71(mark(z0), z1))), MARK(U12(U71(z0, z1))))
   A__U71(tt, U12(length(z0))) -> c32(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0))))
   A__U71(tt, U12(U81(z0))) -> c32(A__LENGTH(a__U12(a__U81(mark(z0)))), MARK(U12(U81(z0))))
   A__U71(tt, U12(U91(z0, z1, z2, z3))) -> c32(A__LENGTH(a__U12(a__U91(mark(z0), z1, z2, z3))), MARK(U12(U91(z0, z1, z2, z3))))
   A__U71(tt, U12(take(z0, z1))) -> c32(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)))), MARK(U12(take(z0, z1))))
   A__U71(tt, U12(and(z0, z1))) -> c32(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1))))
   A__U71(tt, U12(isNatIListKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0))))
   A__U71(tt, U12(isNatKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0))))
   A__U71(tt, U12(cons(z0, z1))) -> c32(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1))))
   A__U71(tt, U12(0)) -> c32(A__LENGTH(a__U12(0)), MARK(U12(0)))
   A__U71(tt, U12(tt)) -> c32(A__LENGTH(a__U12(tt)), MARK(U12(tt)))
   A__U71(tt, U12(s(z0))) -> c32(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U71(tt, U12(nil)) -> c32(A__LENGTH(a__U12(nil)), MARK(U12(nil)))
   A__U71(tt, U12(x0)) -> c32(MARK(U12(x0)))
   A__U71(tt, isNatList(nil)) -> c32(A__LENGTH(tt), MARK(isNatList(nil)))
   A__U71(tt, isNatList(cons(z0, z1))) -> c32(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1))))
   A__U71(tt, isNatList(take(z0, z1))) -> c32(A__LENGTH(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(take(z0, z1))))
   A__U71(tt, isNatList(z0)) -> c32(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_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2


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

(213) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
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   A__U71(tt, isNatList(take(z0, z1))) -> c32(A__LENGTH(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(take(z0, z1))))
   A__U71(tt, isNatList(nil)) -> c32(MARK(isNatList(nil)))
   A__U71(tt, isNatList(z0)) -> c32(MARK(isNatList(z0)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1)))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1))
   MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1)))
   MARK(U11(tt, x1)) -> c68(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c68(MARK(s(z0)))
   MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0)))
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   MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
   MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1))
   MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1)))
   MARK(and(tt, x1)) -> c92(A__AND(tt, x1))
   MARK(and(s(z0), x1)) -> c92(MARK(s(z0)))
   A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(0, z0) -> c64(A__ISNATILIST(z0))
   A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1)))
   A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1)))
   A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1)))
   A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1)))
   A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil)))
   A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros)))
   A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1))))
   A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1))))
   A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0)))
   A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1)))
   A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0)))
   A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0))))
   A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0))))
   A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0)))
   A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1)))
   A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1)))
   A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1)))
   A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1)))
   A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1)))
   A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1)))
   A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1)))
   A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1)))
   A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1)))
   A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1)))
   A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1)))
   A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1)))
   A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1)))
   A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1)))
   A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1)))
   A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1)))
   A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1)))
   A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1)))
   A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1)))
   A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1)))
   A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1)))
   A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1)))
   A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1)))
   A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)))
   A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)))
   A__U71(tt, U12(zeros)) -> c32(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros)))
   A__U71(tt, U12(U11(z0, z1))) -> c32(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U71(tt, U12(U12(z0))) -> c32(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U71(tt, U12(isNatList(z0))) -> c32(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0))))
   A__U71(tt, U12(U21(z0, z1))) -> c32(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1))))
   A__U71(tt, U12(U22(z0))) -> c32(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0))))
   A__U71(tt, U12(isNat(z0))) -> c32(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U71(tt, U12(U31(z0, z1))) -> c32(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U71(tt, U12(U32(z0))) -> c32(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0))))
   A__U71(tt, U12(U41(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U71(tt, U12(U42(z0, z1))) -> c32(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1))))
   A__U71(tt, U12(U43(z0))) -> c32(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0))))
   A__U71(tt, U12(isNatIList(z0))) -> c32(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0))))
   A__U71(tt, U12(U51(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2))))
   A__U71(tt, U12(U52(z0, z1))) -> c32(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1))))
   A__U71(tt, U12(U53(z0))) -> c32(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0))))
   A__U71(tt, U12(U61(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U61(mark(z0), z1, z2))), MARK(U12(U61(z0, z1, z2))))
   A__U71(tt, U12(U62(z0, z1))) -> c32(A__LENGTH(a__U12(a__U62(mark(z0), z1))), MARK(U12(U62(z0, z1))))
   A__U71(tt, U12(U63(z0))) -> c32(A__LENGTH(a__U12(a__U63(mark(z0)))), MARK(U12(U63(z0))))
   A__U71(tt, U12(U71(z0, z1))) -> c32(A__LENGTH(a__U12(a__U71(mark(z0), z1))), MARK(U12(U71(z0, z1))))
   A__U71(tt, U12(length(z0))) -> c32(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0))))
   A__U71(tt, U12(U81(z0))) -> c32(A__LENGTH(a__U12(a__U81(mark(z0)))), MARK(U12(U81(z0))))
   A__U71(tt, U12(U91(z0, z1, z2, z3))) -> c32(A__LENGTH(a__U12(a__U91(mark(z0), z1, z2, z3))), MARK(U12(U91(z0, z1, z2, z3))))
   A__U71(tt, U12(take(z0, z1))) -> c32(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)))), MARK(U12(take(z0, z1))))
   A__U71(tt, U12(and(z0, z1))) -> c32(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1))))
   A__U71(tt, U12(isNatIListKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0))))
   A__U71(tt, U12(isNatKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0))))
   A__U71(tt, U12(cons(z0, z1))) -> c32(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1))))
   A__U71(tt, U12(0)) -> c32(A__LENGTH(a__U12(0)), MARK(U12(0)))
   A__U71(tt, U12(tt)) -> c32(A__LENGTH(a__U12(tt)), MARK(U12(tt)))
   A__U71(tt, U12(s(z0))) -> c32(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U71(tt, U12(nil)) -> c32(A__LENGTH(a__U12(nil)), MARK(U12(nil)))
   A__U71(tt, U12(x0)) -> c32(MARK(U12(x0)))
   A__U71(tt, isNatList(cons(z0, z1))) -> c32(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1))))
   A__U71(tt, isNatList(take(z0, z1))) -> c32(A__LENGTH(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(take(z0, z1))))
   A__U71(tt, isNatList(nil)) -> c32(MARK(isNatList(nil)))
   A__U71(tt, isNatList(z0)) -> c32(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_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2


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

(215) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) by 
   A__U71(tt, U21(x0, z1)) -> c32(A__LENGTH(U21(mark(x0), z1)), MARK(U21(x0, z1)))
   A__U71(tt, U21(zeros, x1)) -> c32(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1)))
   A__U71(tt, U21(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1)))
   A__U71(tt, U21(U12(z0), x1)) -> c32(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1)))
   A__U71(tt, U21(isNatList(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1)))
   A__U71(tt, U21(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1)))
   A__U71(tt, U21(U22(z0), x1)) -> c32(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1)))
   A__U71(tt, U21(isNat(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1)))
   A__U71(tt, U21(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1)))
   A__U71(tt, U21(U32(z0), x1)) -> c32(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1)))
   A__U71(tt, U21(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1)))
   A__U71(tt, U21(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1)))
   A__U71(tt, U21(U43(z0), x1)) -> c32(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1)))
   A__U71(tt, U21(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1)))
   A__U71(tt, U21(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1)))
   A__U71(tt, U21(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1)))
   A__U71(tt, U21(U53(z0), x1)) -> c32(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1)))
   A__U71(tt, U21(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U21(a__U61(mark(z0), z1, z2), x1)), MARK(U21(U61(z0, z1, z2), x1)))
   A__U71(tt, U21(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U62(mark(z0), z1), x1)), MARK(U21(U62(z0, z1), x1)))
   A__U71(tt, U21(U63(z0), x1)) -> c32(A__LENGTH(a__U21(a__U63(mark(z0)), x1)), MARK(U21(U63(z0), x1)))
   A__U71(tt, U21(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U71(mark(z0), z1), x1)), MARK(U21(U71(z0, z1), x1)))
   A__U71(tt, U21(length(z0), x1)) -> c32(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1)))
   A__U71(tt, U21(U81(z0), x1)) -> c32(A__LENGTH(a__U21(a__U81(mark(z0)), x1)), MARK(U21(U81(z0), x1)))
   A__U71(tt, U21(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U21(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U21(take(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1)), MARK(U21(take(z0, z1), x1)))
   A__U71(tt, U21(and(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1)))
   A__U71(tt, U21(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1)))
   A__U71(tt, U21(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1)))
   A__U71(tt, U21(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1)))
   A__U71(tt, U21(0, x1)) -> c32(A__LENGTH(a__U21(0, x1)), MARK(U21(0, x1)))
   A__U71(tt, U21(tt, x1)) -> c32(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1)))
   A__U71(tt, U21(s(z0), x1)) -> c32(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1)))
   A__U71(tt, U21(nil, x1)) -> c32(A__LENGTH(a__U21(nil, x1)), MARK(U21(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
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   A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1)))
   A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1)))
   A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1)))
   A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1)))
   A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1)))
   A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)))
   A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)))
   A__U71(tt, U12(zeros)) -> c32(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros)))
   A__U71(tt, U12(U11(z0, z1))) -> c32(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U71(tt, U12(U12(z0))) -> c32(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U71(tt, U12(isNatList(z0))) -> c32(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0))))
   A__U71(tt, U12(U21(z0, z1))) -> c32(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1))))
   A__U71(tt, U12(U22(z0))) -> c32(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0))))
   A__U71(tt, U12(isNat(z0))) -> c32(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U71(tt, U12(U31(z0, z1))) -> c32(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U71(tt, U12(U32(z0))) -> c32(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0))))
   A__U71(tt, U12(U41(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U71(tt, U12(U42(z0, z1))) -> c32(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1))))
   A__U71(tt, U12(U43(z0))) -> c32(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0))))
   A__U71(tt, U12(isNatIList(z0))) -> c32(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0))))
   A__U71(tt, U12(U51(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2))))
   A__U71(tt, U12(U52(z0, z1))) -> c32(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1))))
   A__U71(tt, U12(U53(z0))) -> c32(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0))))
   A__U71(tt, U12(U61(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U61(mark(z0), z1, z2))), MARK(U12(U61(z0, z1, z2))))
   A__U71(tt, U12(U62(z0, z1))) -> c32(A__LENGTH(a__U12(a__U62(mark(z0), z1))), MARK(U12(U62(z0, z1))))
   A__U71(tt, U12(U63(z0))) -> c32(A__LENGTH(a__U12(a__U63(mark(z0)))), MARK(U12(U63(z0))))
   A__U71(tt, U12(U71(z0, z1))) -> c32(A__LENGTH(a__U12(a__U71(mark(z0), z1))), MARK(U12(U71(z0, z1))))
   A__U71(tt, U12(length(z0))) -> c32(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0))))
   A__U71(tt, U12(U81(z0))) -> c32(A__LENGTH(a__U12(a__U81(mark(z0)))), MARK(U12(U81(z0))))
   A__U71(tt, U12(U91(z0, z1, z2, z3))) -> c32(A__LENGTH(a__U12(a__U91(mark(z0), z1, z2, z3))), MARK(U12(U91(z0, z1, z2, z3))))
   A__U71(tt, U12(take(z0, z1))) -> c32(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)))), MARK(U12(take(z0, z1))))
   A__U71(tt, U12(and(z0, z1))) -> c32(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1))))
   A__U71(tt, U12(isNatIListKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0))))
   A__U71(tt, U12(isNatKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0))))
   A__U71(tt, U12(cons(z0, z1))) -> c32(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1))))
   A__U71(tt, U12(0)) -> c32(A__LENGTH(a__U12(0)), MARK(U12(0)))
   A__U71(tt, U12(tt)) -> c32(A__LENGTH(a__U12(tt)), MARK(U12(tt)))
   A__U71(tt, U12(s(z0))) -> c32(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U71(tt, U12(nil)) -> c32(A__LENGTH(a__U12(nil)), MARK(U12(nil)))
   A__U71(tt, U12(x0)) -> c32(MARK(U12(x0)))
   A__U71(tt, isNatList(cons(z0, z1))) -> c32(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1))))
   A__U71(tt, isNatList(take(z0, z1))) -> c32(A__LENGTH(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(take(z0, z1))))
   A__U71(tt, isNatList(nil)) -> c32(MARK(isNatList(nil)))
   A__U71(tt, isNatList(z0)) -> c32(MARK(isNatList(z0)))
   A__U71(tt, U21(x0, z1)) -> c32(A__LENGTH(U21(mark(x0), z1)), MARK(U21(x0, z1)))
   A__U71(tt, U21(zeros, x1)) -> c32(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1)))
   A__U71(tt, U21(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1)))
   A__U71(tt, U21(U12(z0), x1)) -> c32(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1)))
   A__U71(tt, U21(isNatList(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1)))
   A__U71(tt, U21(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1)))
   A__U71(tt, U21(U22(z0), x1)) -> c32(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1)))
   A__U71(tt, U21(isNat(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1)))
   A__U71(tt, U21(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1)))
   A__U71(tt, U21(U32(z0), x1)) -> c32(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1)))
   A__U71(tt, U21(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1)))
   A__U71(tt, U21(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1)))
   A__U71(tt, U21(U43(z0), x1)) -> c32(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1)))
   A__U71(tt, U21(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1)))
   A__U71(tt, U21(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1)))
   A__U71(tt, U21(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1)))
   A__U71(tt, U21(U53(z0), x1)) -> c32(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1)))
   A__U71(tt, U21(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U21(a__U61(mark(z0), z1, z2), x1)), MARK(U21(U61(z0, z1, z2), x1)))
   A__U71(tt, U21(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U62(mark(z0), z1), x1)), MARK(U21(U62(z0, z1), x1)))
   A__U71(tt, U21(U63(z0), x1)) -> c32(A__LENGTH(a__U21(a__U63(mark(z0)), x1)), MARK(U21(U63(z0), x1)))
   A__U71(tt, U21(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U71(mark(z0), z1), x1)), MARK(U21(U71(z0, z1), x1)))
   A__U71(tt, U21(length(z0), x1)) -> c32(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1)))
   A__U71(tt, U21(U81(z0), x1)) -> c32(A__LENGTH(a__U21(a__U81(mark(z0)), x1)), MARK(U21(U81(z0), x1)))
   A__U71(tt, U21(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U21(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U21(take(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1)), MARK(U21(take(z0, z1), x1)))
   A__U71(tt, U21(and(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1)))
   A__U71(tt, U21(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1)))
   A__U71(tt, U21(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1)))
   A__U71(tt, U21(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1)))
   A__U71(tt, U21(0, x1)) -> c32(A__LENGTH(a__U21(0, x1)), MARK(U21(0, x1)))
   A__U71(tt, U21(tt, x1)) -> c32(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1)))
   A__U71(tt, U21(s(z0), x1)) -> c32(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1)))
   A__U71(tt, U21(nil, x1)) -> c32(A__LENGTH(a__U21(nil, x1)), MARK(U21(nil, x1)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
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   A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1)))
   A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1)))
   A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1)))
   A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1)))
   A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1)))
   A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1)))
   A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1)))
   A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1)))
   A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1)))
   A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1)))
   A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1)))
   A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1)))
   A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1)))
   A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1)))
   A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)))
   A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)))
   A__U71(tt, U12(zeros)) -> c32(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros)))
   A__U71(tt, U12(U11(z0, z1))) -> c32(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U71(tt, U12(U12(z0))) -> c32(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U71(tt, U12(isNatList(z0))) -> c32(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0))))
   A__U71(tt, U12(U21(z0, z1))) -> c32(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1))))
   A__U71(tt, U12(U22(z0))) -> c32(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0))))
   A__U71(tt, U12(isNat(z0))) -> c32(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U71(tt, U12(U31(z0, z1))) -> c32(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U71(tt, U12(U32(z0))) -> c32(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0))))
   A__U71(tt, U12(U41(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U71(tt, U12(U42(z0, z1))) -> c32(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1))))
   A__U71(tt, U12(U43(z0))) -> c32(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0))))
   A__U71(tt, U12(isNatIList(z0))) -> c32(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0))))
   A__U71(tt, U12(U51(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2))))
   A__U71(tt, U12(U52(z0, z1))) -> c32(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1))))
   A__U71(tt, U12(U53(z0))) -> c32(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0))))
   A__U71(tt, U12(U61(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U61(mark(z0), z1, z2))), MARK(U12(U61(z0, z1, z2))))
   A__U71(tt, U12(U62(z0, z1))) -> c32(A__LENGTH(a__U12(a__U62(mark(z0), z1))), MARK(U12(U62(z0, z1))))
   A__U71(tt, U12(U63(z0))) -> c32(A__LENGTH(a__U12(a__U63(mark(z0)))), MARK(U12(U63(z0))))
   A__U71(tt, U12(U71(z0, z1))) -> c32(A__LENGTH(a__U12(a__U71(mark(z0), z1))), MARK(U12(U71(z0, z1))))
   A__U71(tt, U12(length(z0))) -> c32(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0))))
   A__U71(tt, U12(U81(z0))) -> c32(A__LENGTH(a__U12(a__U81(mark(z0)))), MARK(U12(U81(z0))))
   A__U71(tt, U12(U91(z0, z1, z2, z3))) -> c32(A__LENGTH(a__U12(a__U91(mark(z0), z1, z2, z3))), MARK(U12(U91(z0, z1, z2, z3))))
   A__U71(tt, U12(take(z0, z1))) -> c32(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)))), MARK(U12(take(z0, z1))))
   A__U71(tt, U12(and(z0, z1))) -> c32(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1))))
   A__U71(tt, U12(isNatIListKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0))))
   A__U71(tt, U12(isNatKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0))))
   A__U71(tt, U12(cons(z0, z1))) -> c32(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1))))
   A__U71(tt, U12(0)) -> c32(A__LENGTH(a__U12(0)), MARK(U12(0)))
   A__U71(tt, U12(tt)) -> c32(A__LENGTH(a__U12(tt)), MARK(U12(tt)))
   A__U71(tt, U12(s(z0))) -> c32(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U71(tt, U12(nil)) -> c32(A__LENGTH(a__U12(nil)), MARK(U12(nil)))
   A__U71(tt, U12(x0)) -> c32(MARK(U12(x0)))
   A__U71(tt, isNatList(cons(z0, z1))) -> c32(A__LENGTH(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(cons(z0, z1))))
   A__U71(tt, isNatList(take(z0, z1))) -> c32(A__LENGTH(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)), MARK(isNatList(take(z0, z1))))
   A__U71(tt, isNatList(nil)) -> c32(MARK(isNatList(nil)))
   A__U71(tt, isNatList(z0)) -> c32(MARK(isNatList(z0)))
   A__U71(tt, U21(x0, z1)) -> c32(A__LENGTH(U21(mark(x0), z1)), MARK(U21(x0, z1)))
   A__U71(tt, U21(zeros, x1)) -> c32(A__LENGTH(a__U21(a__zeros, x1)), MARK(U21(zeros, x1)))
   A__U71(tt, U21(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U11(mark(z0), z1), x1)), MARK(U21(U11(z0, z1), x1)))
   A__U71(tt, U21(U12(z0), x1)) -> c32(A__LENGTH(a__U21(a__U12(mark(z0)), x1)), MARK(U21(U12(z0), x1)))
   A__U71(tt, U21(isNatList(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatList(z0), x1)), MARK(U21(isNatList(z0), x1)))
   A__U71(tt, U21(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U21(mark(z0), z1), x1)), MARK(U21(U21(z0, z1), x1)))
   A__U71(tt, U21(U22(z0), x1)) -> c32(A__LENGTH(a__U21(a__U22(mark(z0)), x1)), MARK(U21(U22(z0), x1)))
   A__U71(tt, U21(isNat(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNat(z0), x1)), MARK(U21(isNat(z0), x1)))
   A__U71(tt, U21(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1)))
   A__U71(tt, U21(U32(z0), x1)) -> c32(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1)))
   A__U71(tt, U21(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1)))
   A__U71(tt, U21(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1)))
   A__U71(tt, U21(U43(z0), x1)) -> c32(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1)))
   A__U71(tt, U21(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1)))
   A__U71(tt, U21(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1)))
   A__U71(tt, U21(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1)))
   A__U71(tt, U21(U53(z0), x1)) -> c32(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1)))
   A__U71(tt, U21(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U21(a__U61(mark(z0), z1, z2), x1)), MARK(U21(U61(z0, z1, z2), x1)))
   A__U71(tt, U21(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U62(mark(z0), z1), x1)), MARK(U21(U62(z0, z1), x1)))
   A__U71(tt, U21(U63(z0), x1)) -> c32(A__LENGTH(a__U21(a__U63(mark(z0)), x1)), MARK(U21(U63(z0), x1)))
   A__U71(tt, U21(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U71(mark(z0), z1), x1)), MARK(U21(U71(z0, z1), x1)))
   A__U71(tt, U21(length(z0), x1)) -> c32(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1)))
   A__U71(tt, U21(U81(z0), x1)) -> c32(A__LENGTH(a__U21(a__U81(mark(z0)), x1)), MARK(U21(U81(z0), x1)))
   A__U71(tt, U21(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U21(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U21(take(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1)), MARK(U21(take(z0, z1), x1)))
   A__U71(tt, U21(and(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1)))
   A__U71(tt, U21(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1)))
   A__U71(tt, U21(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1)))
   A__U71(tt, U21(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1)))
   A__U71(tt, U21(0, x1)) -> c32(A__LENGTH(a__U21(0, x1)), MARK(U21(0, x1)))
   A__U71(tt, U21(tt, x1)) -> c32(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1)))
   A__U71(tt, U21(s(z0), x1)) -> c32(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1)))
   A__U71(tt, U21(nil, x1)) -> c32(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_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2


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

(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, z1) -> a__U62(a__isNat(z0), z1)
   a__U61(z0, z1, z2) -> U61(z0, z1, z2)
   a__U62(tt, z0) -> a__U63(a__isNatIList(z0))
   a__U62(z0, z1) -> U62(z0, z1)
   a__U63(tt) -> tt
   a__U63(z0) -> U63(z0)
   a__U71(tt, z0) -> s(a__length(mark(z0)))
   a__U71(z0, z1) -> U71(z0, z1)
   a__U81(tt) -> nil
   a__U81(z0) -> U81(z0)
   a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0))
   a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3)
   a__and(tt, z0) -> mark(z0)
   a__and(z0, z1) -> and(z0, z1)
   a__isNat(0) -> tt
   a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0)
   a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0)
   a__isNat(z0) -> isNat(z0)
   a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0)
   a__isNatIList(zeros) -> tt
   a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatIList(z0) -> isNatIList(z0)
   a__isNatIListKind(nil) -> tt
   a__isNatIListKind(zeros) -> tt
   a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1))
   a__isNatIListKind(z0) -> isNatIListKind(z0)
   a__isNatKind(0) -> tt
   a__isNatKind(length(z0)) -> a__isNatIListKind(z0)
   a__isNatKind(s(z0)) -> a__isNatKind(z0)
   a__isNatKind(z0) -> isNatKind(z0)
   a__isNatList(nil) -> tt
   a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1)
   a__isNatList(z0) -> isNatList(z0)
   a__length(nil) -> 0
   a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1)
   a__length(z0) -> length(z0)
   a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0)))
   a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1)
   a__take(z0, z1) -> take(z0, z1)
   mark(zeros) -> a__zeros
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNatList(z0)) -> a__isNatList(z0)
   mark(U21(z0, z1)) -> a__U21(mark(z0), z1)
   mark(U22(z0)) -> a__U22(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U32(z0)) -> a__U32(mark(z0))
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1)) -> a__U42(mark(z0), z1)
   mark(U43(z0)) -> a__U43(mark(z0))
   mark(isNatIList(z0)) -> a__isNatIList(z0)
   mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2)
   mark(U52(z0, z1)) -> a__U52(mark(z0), z1)
   mark(U53(z0)) -> a__U53(mark(z0))
   mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2)
   mark(U62(z0, z1)) -> a__U62(mark(z0), z1)
   mark(U63(z0)) -> a__U63(mark(z0))
   mark(U71(z0, z1)) -> a__U71(mark(z0), z1)
   mark(length(z0)) -> a__length(mark(z0))
   mark(U81(z0)) -> a__U81(mark(z0))
   mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3)
   mark(take(z0, z1)) -> a__take(mark(z0), mark(z1))
   mark(and(z0, z1)) -> a__and(mark(z0), z1)
   mark(isNatIListKind(z0)) -> a__isNatIListKind(z0)
   mark(isNatKind(z0)) -> a__isNatKind(z0)
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(0) -> 0
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(nil) -> nil
Tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
   MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1)))
   MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0)))
   MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1)))
   MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0)))
   MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0)))
   MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3)))
   MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1)))
   MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1)))
   MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0)))
   MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0)))
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   A__U71(tt, U21(U53(z0), x1)) -> c32(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1)))
   A__U71(tt, U21(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U21(a__U61(mark(z0), z1, z2), x1)), MARK(U21(U61(z0, z1, z2), x1)))
   A__U71(tt, U21(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U62(mark(z0), z1), x1)), MARK(U21(U62(z0, z1), x1)))
   A__U71(tt, U21(U63(z0), x1)) -> c32(A__LENGTH(a__U21(a__U63(mark(z0)), x1)), MARK(U21(U63(z0), x1)))
   A__U71(tt, U21(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U71(mark(z0), z1), x1)), MARK(U21(U71(z0, z1), x1)))
   A__U71(tt, U21(length(z0), x1)) -> c32(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1)))
   A__U71(tt, U21(U81(z0), x1)) -> c32(A__LENGTH(a__U21(a__U81(mark(z0)), x1)), MARK(U21(U81(z0), x1)))
   A__U71(tt, U21(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U21(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U21(take(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1)), MARK(U21(take(z0, z1), x1)))
   A__U71(tt, U21(and(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1)))
   A__U71(tt, U21(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1)))
   A__U71(tt, U21(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1)))
   A__U71(tt, U21(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1)))
   A__U71(tt, U21(tt, x1)) -> c32(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1)))
   A__U71(tt, U21(s(z0), x1)) -> c32(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1)))
   A__U71(tt, U21(x0, z1)) -> c32(MARK(U21(x0, z1)))
   A__U71(tt, U21(0, x1)) -> c32(A__LENGTH(a__U21(0, x1)))
   A__U71(tt, U21(nil, x1)) -> c32(A__LENGTH(a__U21(nil, x1)))
S tuples:
   A__U91(tt, z0, z1, z2) -> c36(MARK(z2))
   A__AND(tt, z0) -> c38(MARK(z0))
   A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0))
   A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0))
   MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0))
   MARK(isNat(z0)) -> c73(A__ISNAT(z0))
   MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0))
   MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0))
   MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0))
   MARK(cons(z0, z1)) -> c95(MARK(z0))
   MARK(s(z0)) -> c98(MARK(z0))
   A__U11(tt, z0) -> c2(A__ISNATLIST(z0))
   A__U21(tt, z0) -> c6(A__ISNAT(z0))
   A__U31(tt, z0) -> c10(A__ISNATLIST(z0))
   A__U42(tt, z0) -> c16(A__ISNATILIST(z0))
   A__U52(tt, z0) -> c22(A__ISNATLIST(z0))
   A__U62(tt, z0) -> c28(A__ISNATILIST(z0))
   MARK(U12(z0)) -> c69(MARK(z0))
   MARK(U22(z0)) -> c72(MARK(z0))
   MARK(U32(z0)) -> c75(MARK(z0))
   MARK(U43(z0)) -> c78(MARK(z0))
   MARK(U53(z0)) -> c82(MARK(z0))
   MARK(U63(z0)) -> c85(MARK(z0))
   MARK(U81(z0)) -> c88(MARK(z0))
   A__U41(tt, 0, x1) -> c14(A__U42(tt, x1))
   A__U41(tt, z0, x1) -> c14(A__ISNAT(z0))
   A__U51(tt, 0, x1) -> c20(A__U52(tt, x1))
   A__U51(tt, z0, x1) -> c20(A__ISNAT(z0))
   A__U61(tt, 0, x1) -> c26(A__U62(tt, x1))
   A__U61(tt, z0, x1) -> c26(A__ISNAT(z0))
   A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0)))
   A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0)))
   A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0)))
   A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1)))
   A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0)))
   A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0)))
   A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2)))
   A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1)))
   A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0)))
   A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2)))
   A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1)))
   A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0)))
   A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1)))
   A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0)))
   A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0)))
   A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3)))
   A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1)))
   A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1)))
   A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0)))
   A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0)))
   A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1)))
   A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros))
   A__U71(tt, s(z0)) -> c32(MARK(s(z0)))
   A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNAT(length(nil)) -> c41(A__U11(tt, nil))
   A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros))
   A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0))
   A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0)))
   A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0)))
   A__ISNAT(s(0)) -> c42(A__U21(tt, 0))
   A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0))
   A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1)))
   A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1)))
   A__ISNATILIST(nil) -> c44(A__U31(tt, nil))
   A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros))
   A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0))
   A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0))
   A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)))
   A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0))
   A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0)))
   A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0)))
   A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0))
   A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0))
   A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)))
   A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1)))
   A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1)))
   A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0))
   A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1))
   A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros))
   A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1)))
   A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0))
   A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2))
   MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0)))
   MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1)))
   MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0)))
   MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1)))
   MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0)))
   MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0)))
   MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2)))
   MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1)))
   MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0)))
   MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2)))
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   A__U71(tt, U21(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U31(mark(z0), z1), x1)), MARK(U21(U31(z0, z1), x1)))
   A__U71(tt, U21(U32(z0), x1)) -> c32(A__LENGTH(a__U21(a__U32(mark(z0)), x1)), MARK(U21(U32(z0), x1)))
   A__U71(tt, U21(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U21(a__U41(mark(z0), z1, z2), x1)), MARK(U21(U41(z0, z1, z2), x1)))
   A__U71(tt, U21(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U42(mark(z0), z1), x1)), MARK(U21(U42(z0, z1), x1)))
   A__U71(tt, U21(U43(z0), x1)) -> c32(A__LENGTH(a__U21(a__U43(mark(z0)), x1)), MARK(U21(U43(z0), x1)))
   A__U71(tt, U21(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatIList(z0), x1)), MARK(U21(isNatIList(z0), x1)))
   A__U71(tt, U21(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U21(a__U51(mark(z0), z1, z2), x1)), MARK(U21(U51(z0, z1, z2), x1)))
   A__U71(tt, U21(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U52(mark(z0), z1), x1)), MARK(U21(U52(z0, z1), x1)))
   A__U71(tt, U21(U53(z0), x1)) -> c32(A__LENGTH(a__U21(a__U53(mark(z0)), x1)), MARK(U21(U53(z0), x1)))
   A__U71(tt, U21(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U21(a__U61(mark(z0), z1, z2), x1)), MARK(U21(U61(z0, z1, z2), x1)))
   A__U71(tt, U21(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U62(mark(z0), z1), x1)), MARK(U21(U62(z0, z1), x1)))
   A__U71(tt, U21(U63(z0), x1)) -> c32(A__LENGTH(a__U21(a__U63(mark(z0)), x1)), MARK(U21(U63(z0), x1)))
   A__U71(tt, U21(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__U71(mark(z0), z1), x1)), MARK(U21(U71(z0, z1), x1)))
   A__U71(tt, U21(length(z0), x1)) -> c32(A__LENGTH(a__U21(a__length(mark(z0)), x1)), MARK(U21(length(z0), x1)))
   A__U71(tt, U21(U81(z0), x1)) -> c32(A__LENGTH(a__U21(a__U81(mark(z0)), x1)), MARK(U21(U81(z0), x1)))
   A__U71(tt, U21(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U21(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U21(U91(z0, z1, z2, z3), x1)))
   A__U71(tt, U21(take(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__take(mark(z0), mark(z1)), x1)), MARK(U21(take(z0, z1), x1)))
   A__U71(tt, U21(and(z0, z1), x1)) -> c32(A__LENGTH(a__U21(a__and(mark(z0), z1), x1)), MARK(U21(and(z0, z1), x1)))
   A__U71(tt, U21(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatIListKind(z0), x1)), MARK(U21(isNatIListKind(z0), x1)))
   A__U71(tt, U21(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U21(a__isNatKind(z0), x1)), MARK(U21(isNatKind(z0), x1)))
   A__U71(tt, U21(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U21(cons(mark(z0), z1), x1)), MARK(U21(cons(z0, z1), x1)))
   A__U71(tt, U21(tt, x1)) -> c32(A__LENGTH(a__U21(tt, x1)), MARK(U21(tt, x1)))
   A__U71(tt, U21(s(z0), x1)) -> c32(A__LENGTH(a__U21(s(mark(z0)), x1)), MARK(U21(s(z0), x1)))
   A__U71(tt, U21(x0, z1)) -> c32(MARK(U21(x0, z1)))
   A__U71(tt, U21(0, x1)) -> c32(A__LENGTH(a__U21(0, x1)))
   A__U71(tt, U21(nil, x1)) -> c32(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_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1

Defined Pair Symbols:   A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2

Compound Symbols:   c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2